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Journal articles on the topic 'Discontinuous spectral element method'

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Author: Grafiati

Published: 10 December 2022

Last updated: 29 January 2023

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1

Shi1, Xing, Jianzhong Lin, and Zhaosheng Yu. "Discontinuous Galerkin spectral element lattice Boltzmann method on triangular element." International Journal for Numerical Methods in Fluids 42, no. 11 (2003): 1249–61. http://dx.doi.org/10.1002/fld.594.

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2

Pei, Chaoxu, Mark Sussman, and M. Yousuff Hussaini. "A Space-Time Discontinuous Galerkin Spectral Element Method for Nonlinear Hyperbolic Problems." International Journal of Computational Methods 16, no. 01 (November 21, 2018): 1850093. http://dx.doi.org/10.1142/s0219876218500937.

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A space-time discontinuous Galerkin spectral element method is combined with two different approaches for treating problems with discontinuous solutions: (i) adding a space-time dependent artificial viscosity, and (ii) tracking the discontinuity with space-time spectral accuracy. A Picard iteration method is employed to solve nonlinear system of equations derived from the space-time DG spectral element discretization. Spectral accuracy in both space and time is demonstrated for the Burgers’ equation with a smooth solution. For tests with discontinuities, the present space-time method enables better accuracy at capturing the shock strength in the element containing shock when higher order polynomials in both space and time are used. The spectral accuracy of the shock speed and location is demonstrated for the solution of the inviscid Burgers’ equation obtained by the tracking method.

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3

Gassner, Gregor J. "A kinetic energy preserving nodal discontinuous Galerkin spectral element method." International Journal for Numerical Methods in Fluids 76, no. 1 (June 10, 2014): 28–50. http://dx.doi.org/10.1002/fld.3923.

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4

Zayernouri, Mohsen, Wanrong Cao, Zhongqiang Zhang, and George Em Karniadakis. "Spectral and Discontinuous Spectral Element Methods for Fractional Delay Equations." SIAM Journal on Scientific Computing 36, no. 6 (January 2014): B904—B929. http://dx.doi.org/10.1137/130935884.

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5

Hessari, Peyman, Sang Dong Kim, and Byeong-Chun Shin. "Numerical Solution for Elliptic Interface Problems Using Spectral Element Collocation Method." Abstract and Applied Analysis 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/780769.

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The aim of this paper is to solve an elliptic interface problem with a discontinuous coefficient and a singular source term by the spectral collocation method. First, we develop an algorithm for the elliptic interface problem defined in a rectangular domain with a line interface. By using the Gordon-Hall transformation, we generalize it to a domain with a curve boundary and a curve interface. The spectral element collocation method is then employed to complex geometries; that is, we decompose the domain into some nonoverlaping subdomains and the spectral collocation solution is sought in each subdomain. We give some numerical experiments to show efficiency of our algorithm and its spectral convergence.

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6

Peyvan, Ahmad, Jonathan Komperda, Dongru Li, Zia Ghiasi, and Farzad Mashayek. "Flux reconstruction using Jacobi correction functions in discontinuous spectral element method." Journal of Computational Physics 435 (June 2021): 110261. http://dx.doi.org/10.1016/j.jcp.2021.110261.

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7

Zhao, J. M., and L. H. Liu. "Three-Dimensional Transient Radiative Transfer Modeling Using Discontinuous Spectral Element Method." Journal of Thermophysics and Heat Transfer 23, no. 4 (October 2009): 836–40. http://dx.doi.org/10.2514/1.39361.

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8

Kopriva, David A. "Metric Identities and the Discontinuous Spectral Element Method on Curvilinear Meshes." Journal of Scientific Computing 26, no. 3 (March 2006): 301–27. http://dx.doi.org/10.1007/s10915-005-9070-8.

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9

Pei, Chaoxu, Mark Sussman, and M. Yousuff Hussaini. "A space-time discontinuous Galerkin spectral element method for the Stefan problem." Discrete & Continuous Dynamical Systems - B 23, no. 9 (2018): 3595–622. http://dx.doi.org/10.3934/dcdsb.2017216.

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10

Joon-Ho Lee, Jiefu Chen, and Qing Huo Liu. "A 3-D Discontinuous Spectral Element Time-Domain Method for Maxwell's Equations." IEEE Transactions on Antennas and Propagation 57, no. 9 (September 2009): 2666–74. http://dx.doi.org/10.1109/tap.2009.2027731.

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11

Wang, Wen-Kai, Rui-Rui Zhou, and Ben-Wen Li. "Discontinuous spectral element method for radiative heat transfer in axisymmetric cylindrical medium." Journal of Quantitative Spectroscopy and Radiative Transfer 226 (March 2019): 29–39. http://dx.doi.org/10.1016/j.jqsrt.2019.01.007.

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12

Pacciarini, Paolo, Paola Gervasio, and Alfio Quarteroni. "Spectral based Discontinuous Galerkin Reduced Basis Element method for parametrized Stokes problems." Computers & Mathematics with Applications 72, no. 8 (October 2016): 1977–87. http://dx.doi.org/10.1016/j.camwa.2016.01.030.

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13

Rueda-Ramírez, Andrés M., Gonzalo Rubio, Esteban Ferrer, and Eusebio Valero. "Truncation Error Estimation in the p-Anisotropic Discontinuous Galerkin Spectral Element Method." Journal of Scientific Computing 78, no. 1 (July 2, 2018): 433–66. http://dx.doi.org/10.1007/s10915-018-0772-0.

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14

Madaule, Éric, Marco Restelli, and Eric Sonnendrücker. "Energy conserving discontinuous Galerkin spectral element method for the Vlasov–Poisson system." Journal of Computational Physics 279 (December 2014): 261–88. http://dx.doi.org/10.1016/j.jcp.2014.09.010.

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15

Min, Misun, and Taehun Lee. "A spectral-element discontinuous Galerkin lattice Boltzmann method for nearly incompressible flows." Journal of Computational Physics 230, no. 1 (January 2011): 245–59. http://dx.doi.org/10.1016/j.jcp.2010.09.024.

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16

Ghiasi, Zia, Jonathan Komperda, Dongru Li, Ahmad Peyvan, David Nicholls, and Farzad Mashayek. "Modal explicit filtering for large eddy simulation in discontinuous spectral element method." Journal of Computational Physics: X 3 (June 2019): 100024. http://dx.doi.org/10.1016/j.jcpx.2019.100024.

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17

Kopriva, David A., Stephen L. Woodruff, and M. Y. Hussaini. "Computation of electromagnetic scattering with a non-conforming discontinuous spectral element method." International Journal for Numerical Methods in Engineering 53, no. 1 (2001): 105–22. http://dx.doi.org/10.1002/nme.394.

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18

Baldassari, Caroline, Hélène Barucq, Henri Calandra, Bertrand Denel, and Julien Diaz. "Performance Analysis of a High-Order Discontinuous Galerkin Method Application to the Reverse Time Migration." Communications in Computational Physics 11, no. 2 (February 2012): 660–73. http://dx.doi.org/10.4208/cicp.291209.171210s.

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AbstractThis work pertains to numerical aspects of a finite element method based discontinuous functions. Our study focuses on the Interior Penalty Discontinuous Galerkin method (IPDGM) because of its high-level of flexibility for solving the full wave equation in heterogeneous media. We assess the performance of IPDGM through a comparison study with a spectral element method (SEM). We show that IPDGM is as accurate as SEM. In addition, we illustrate the efficiency of IPDGM when employed in a seismic imaging process by considering two-dimensional problems involving the Reverse Time Migration.

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19

Zhao, Jiazi, Yasong Sun, Yifan Li, and Changhao Liu. "Investigation of coupled radiation-conduction heat transfer in cylindrical systems by discontinuous spectral element method." Journal of the Global Power and Propulsion Society 6 (December 30, 2022): 354–66. http://dx.doi.org/10.33737/jgpps/156350.

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Nowadays, in order to achieve higher efficiency in aero-engines, the increase of turbine inlet temperature in aero-engine is in urgent need. At present, the turbine inlet temperature is around 2,000 K, which means the radiation and coupled radiation-conduction heat transfer play more and more important roles in hot section of aero-engines. As we all konw, considering the cylindrical symmetry of aero-engines. It is convenient to adopt the cylindrical coordinate to simplify the description of these systems, such as annular combustor, exhaust nozzle, etc. In this paper, Discontinuous Spectral Element Method (DSEM) is extended to solve the radiation and coupled radiation-coduction heat transfer in cylindrical coordinate system. Both the spatial and angular computational domains of radiative transfer equation (RTE) are discretized and solved by DSEM. For coupled radiation-conduction heat transfer problem, Discontinuous Spectral Element Method-Spectral Element Method (DSEM-SEM) scheme is used to avoid using two sets of grid which would cause the increase of computational cost and the decrease of accuracy. Then, the effects of various geometric and thermal physical parameters are comprehensively investigated. Finally, these methods are further extended to 2D cylindrical system.

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20

Pranowo, Pranowo, and Djoko Budiyanto Setyohadi. "Numerical simulation of electromagnetic radiation using high-order discontinuous galerkin time domain method." International Journal of Electrical and Computer Engineering (IJECE) 9, no. 2 (April 1, 2019): 1267. http://dx.doi.org/10.11591/ijece.v9i2.pp1267-1274.

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<span>In this paper, we propose the simulation of 2-dimensional electromagnetic wave radiation using high-order discontinuous Galerkin time domain method to solve Maxwell's equations. The domains are discretized into unstructured straight-sided triangle elements that allow enhanced flexibility when dealing with complex geometries. The electric and magnetic fields are expanded into a high-order polynomial spectral approximation over each triangle element. The field conservation between the elements is enforced using central difference flux calculation at element interfaces. Perfectly matched layer (PML) boundary condition is used to absorb the waves that leave the domain. The comparison of numerical calculations is performed by the graphical displays and numerical data of radiation phenomenon and presented particularly with the results of the FDTD method. Finally, our simulations show that the proposed method can handle simulation of electromagnetic radiation with complex geometries easily.</span>

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21

Antonietti, Paola F., Alberto Ferroni, Ilario Mazzieri, Roberto Paolucci, Alfio Quarteroni, Chiara Smerzini, and Marco Stupazzini. "Numerical modeling of seismic waves by discontinuous spectral element methods." ESAIM: Proceedings and Surveys 61 (2018): 1–37. http://dx.doi.org/10.1051/proc/201861001.

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We present a comprehensive review of Discontinuous Galerkin Spectral Element (DGSE) methods on hybrid hexahedral/tetrahedral grids for the numerical modeling of the ground motion induced by large earthquakes. DGSE methods combine the exibility of discontinuous Galerkin meth-ods to patch together, through a domain decomposition paradigm, Spectral Element blocks where high-order polynomials are used for the space discretization. This approach allows local adaptivity on discretization parameters, thus improving the quality of the solution without affecting the compu-tational costs. The theoretical properties of the semidiscrete formulation are also revised, including well-posedness, stability and error estimates. A discussion on the dissipation, dispersion and stability properties of the fully-discrete (in space and time) formulation is also presented. Here space dis-cretization is obtained based on employing the leap-frog time marching scheme. The capabilities of the present approach are demonstrated through a set of computations of realistic earthquake scenar-ios obtained using the code SPEED (http://speed.mox.polimi.it), an open-source code specifically designed for the numerical modeling of large-scale seismic events jointly developed at Politecnico di Milano by The Laboratory for Modeling and Scientific Computing MOX and by the Department of Civil and Environmental Engineering.

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22

BERNARDI, CHRISTINE, and NEJMEDDINE CHORFI. "MORTAR SPECTRAL ELEMENT METHODS FOR ELLIPTIC EQUATIONS WITH DISCONTINUOUS COEFFICIENTS." Mathematical Models and Methods in Applied Sciences 12, no. 04 (April 2002): 497–524. http://dx.doi.org/10.1142/s0218202502001763.

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We consider a second-order elliptic equation with piecewise continuous coefficients in a bounded two-dimensional domain. We propose a spectral element discretization of this problem which relies on the mortar domain decomposition technique. We prove optimal error estimates. Next, we compare several versions, conforming or not, of this discretization by means of numerical experiments.

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23

Cao, Zhoujian, Pei Fu, Li-Wei Ji, and Yinhua Xia. "Application of local discontinuous Galerkin method to Einstein equations." International Journal of Modern Physics D 28, no. 01 (January 2019): 1950014. http://dx.doi.org/10.1142/s0218271819500147.

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Finite difference and pseudo-spectral methods have been widely used in the numerical relativity to solve the Einstein equations. As the third major category method to solve partial differential equations, finite element method is less frequently used in numerical relativity. In this paper, we design a finite element algorithm to solve the evolution part of the Einstein equations. This paper is the second one of a systematic investigation of applying adaptive finite element method to the Einstein equations, especially aiming for binary compact objects simulations. The first paper of this series has been contributed to the constrained part of the Einstein equations for initial data. Since applying finite element method to the Einstein equations is a big project, we mainly propose the theoretical framework of a finite element algorithm together with local discontinuous Galerkin method for the Einstein equations in the current work. In addition, we have tested our algorithm based on the spherical symmetric spacetime evolution. In order to simplify our numerical tests, we have reduced the problem to a one-dimensional space problem by taking the advantage of the spherical symmetry. Our reduced equation system is a new formalism for spherical symmetric spacetime simulation. Based on our test results, we find that our finite element method can capture the shock formation which is introduced by numerical error. In contrast, such shock is smoothed out by numerical dissipation within the finite difference method. We suspect this is partly the reason that the accuracy of finite element method is higher than the finite difference method. At the same time, different kinds of formulation parameters setting are also discussed.

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24

Zhao, J. M., and L. H. Liu. "Discontinuous spectral element method for solving radiative heat transfer in multidimensional semitransparent media." Journal of Quantitative Spectroscopy and Radiative Transfer 107, no. 1 (September 2007): 1–16. http://dx.doi.org/10.1016/j.jqsrt.2007.02.001.

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25

Lehotzky, David, Tamas Insperger, Firas Khasawneh, and Gabor Stepan. "Spectral element method for stability analysis of milling processes with discontinuous time-periodicity." International Journal of Advanced Manufacturing Technology 89, no. 9-12 (June 22, 2016): 2503–14. http://dx.doi.org/10.1007/s00170-016-9044-z.

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26

Gerritsma, Marc I. "Direct Minimization of the Discontinuous Least-Squares Spectral Element Method for Viscoelastic Fluids." Journal of Scientific Computing 27, no. 1-3 (March 13, 2006): 245–56. http://dx.doi.org/10.1007/s10915-005-9042-z.

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27

Bui-Thanh, Tan, and Omar Ghattas. "Analysis of an $hp$-Nonconforming Discontinuous Galerkin Spectral Element Method for Wave Propagation." SIAM Journal on Numerical Analysis 50, no. 3 (January 2012): 1801–26. http://dx.doi.org/10.1137/110828010.

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28

Kopriva, David A. "Stability of Overintegration Methods for Nodal Discontinuous Galerkin Spectral Element Methods." Journal of Scientific Computing 76, no. 1 (December 7, 2017): 426–42. http://dx.doi.org/10.1007/s10915-017-0626-1.

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29

Rivas-Ortiz, Iram Barbaro, Dany Sanchez Dominguez, Carlos Rafael Garcia Hernandez, Susana Marrero Iglesias, and Alberto Escrivá. "An Extended Linear Discontinuous Method for One-group Fixed Source Discrete Ordinates Problems with Isotropic Scattering in Slab Geometry." TEMA (São Carlos) 20, no. 1 (May 20, 2019): 61. http://dx.doi.org/10.5540/tema.2019.020.01.61.

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Nowadays, the obtainment of an accurate numerical solution of fixed source discrete ordinates problems is relevant in many areas of engineering and science. In this work, we extend the hybrid Finite Element Spectral Green's Function method (FEM-SGF), originally developed to solve eigenvalue diffusion problems, for fixed source problems using as a mathematical model, the discrete ordinates formulation in one energy group with isotropic scattering in slab geometry. This new method, Extended Linear Discontinuous Discrete Ordinates (ELD-SN), is based on the use of neutron balance equations and the construction of a hybrid auxiliary equation. This auxiliary equation combines a linear discontinuous approximation and spectral parameters to approximate the neutron angular flux inside the cell. Numerical results for benchmark problems are presented to illustrate the accuracy and computational performance of our methodology. ELD-SN method is free from spatial truncation errors in S2 quadrature, and generate good results in the other quadrature sets. This method is more accurate than the conventional Diamond Difference (DD) and Linear Discontinuous (LD) methods, but surpassed by the Spectral Green's Function (SGF) method, for quadrature order greater than two.

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30

Dzanic, T., and F. D. Witherden. "Positivity-preserving entropy-based adaptive filtering for discontinuous spectral element methods." Journal of Computational Physics 468 (November 2022): 111501. http://dx.doi.org/10.1016/j.jcp.2022.111501.

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31

Zayernouri, Mohsen, and George Em Karniadakis. "Discontinuous Spectral Element Methods for Time- and Space-Fractional Advection Equations." SIAM Journal on Scientific Computing 36, no. 4 (January 2014): B684—B707. http://dx.doi.org/10.1137/130940967.

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32

Peyvan, Ahmad, Dongru Li, Jonathan Komperda, and Farzad Mashayek. "Oscillation-free nodal discontinuous spectral element method for the simulation of compressible multicomponent flows." Journal of Computational Physics 452 (March 2022): 110921. http://dx.doi.org/10.1016/j.jcp.2021.110921.

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33

Deng, Shaozhong, and Wei Cai. "Discontinuous spectral element method modeling of optical coupling by whispering gallery modes between microcylinders." Journal of the Optical Society of America A 22, no. 5 (May 1, 2005): 952. http://dx.doi.org/10.1364/josaa.22.000952.

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34

Abbassi, Hesam, Farzad Mashayek, and Gustaaf B. Jacobs. "Shock capturing with entropy-based artificial viscosity for staggered grid discontinuous spectral element method." Computers & Fluids 98 (July 2014): 152–63. http://dx.doi.org/10.1016/j.compfluid.2014.01.022.

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35

Patel, Saumil, Misun Min, and Taehun Lee. "A spectral-element discontinuous Galerkin thermal lattice Boltzmann method for conjugate heat transfer applications." International Journal for Numerical Methods in Fluids 82, no. 12 (May 29, 2016): 932–52. http://dx.doi.org/10.1002/fld.4250.

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36

Gavrilieva, Uygulana, Maria Vasilyeva, and Eric T. Chung. "Generalized Multiscale Finite Element Method for Elastic Wave Propagation in the Frequency Domain." Computation 8, no. 3 (July 7, 2020): 63. http://dx.doi.org/10.3390/computation8030063.

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In this work, we consider elastic wave propagation in fractured media. The mathematical model is described by the Helmholtz problem related to wave propagation with specific interface conditions (Linear Slip Model, LSM) on the fracture in the frequency domain. For the numerical solution, we construct a fine grid that resolves all fracture interfaces on the grid level and construct approximation using a finite element method. We use a discontinuous Galerkin method for the approximation by space that helps to weakly impose interface conditions on fractures. Such approximation leads to a large system of equations and is computationally expensive. In this work, we construct a coarse grid approximation for an effective solution using the Generalized Multiscale Finite Element Method (GMsFEM). We construct and compare two types of the multiscale methods—Continuous Galerkin Generalized Multiscale Finite Element Method (CG-GMsFEM) and Discontinuous Galerkin Generalized Multiscale Finite Element Method (DG-GMsFEM). Multiscale basis functions are constructed by solving local spectral problems in each local domains to extract dominant modes of the local solution. In CG-GMsFEM, we construct continuous multiscale basis functions that are defined in the local domains associated with the coarse grid node and contain four coarse grid cells for the structured quadratic coarse grid. The multiscale basis functions in DG-GMsFEM are discontinuous and defined in each coarse grid cell. The results of the numerical solution for the two-dimensional Helmholtz equation are presented for CG-GMsFEM and DG-GMsFEM for different numbers of multiscale basis functions.

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37

Guerra, Jorge E., and Paul A. Ullrich. "A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models." Geoscientific Model Development 9, no. 5 (June 1, 2016): 2007–29. http://dx.doi.org/10.5194/gmd-9-2007-2016.

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Abstract. Atmospheric modeling systems require economical methods to solve the non-hydrostatic Euler equations. Two major differences between hydrostatic models and a full non-hydrostatic description lies in the vertical velocity tendency and numerical stiffness associated with sound waves. In this work we introduce a new arbitrary-order vertical discretization entitled the staggered nodal finite-element method (SNFEM). Our method uses a generalized discrete derivative that consistently combines the discontinuous Galerkin and spectral element methods on a staggered grid. Our combined method leverages the accurate wave propagation and conservation properties of spectral elements with staggered methods that eliminate stationary (2Δx) modes. Furthermore, high-order accuracy also eliminates the need for a reference state to maintain hydrostatic balance. In this work we demonstrate the use of high vertical order as a means of improving simulation quality at relatively coarse resolution. We choose a test case suite that spans the range of atmospheric flows from predominantly hydrostatic to nonlinear in the large-eddy regime. Our results show that there is a distinct benefit in using the high-order vertical coordinate at low resolutions with the same robust properties as the low-order alternative.

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38

Chaudhuri, A., G. B. Jacobs, W. S. Don, H. Abbassi, and F. Mashayek. "Explicit discontinuous spectral element method with entropy generation based artificial viscosity for shocked viscous flows." Journal of Computational Physics 332 (March 2017): 99–117. http://dx.doi.org/10.1016/j.jcp.2016.11.042.

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39

Taneja, Ankur, and Jonathan Higdon. "A fully-coupled discontinuous Galerkin spectral element method for two-phase flow in petroleum reservoirs." Journal of Computational Physics 352 (January 2018): 341–72. http://dx.doi.org/10.1016/j.jcp.2017.09.059.

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40

Min, Misun, and Paul Fischer. "An Efficient High-Order Time Integration Method for Spectral-Element Discontinuous Galerkin Simulations in Electromagnetics." Journal of Scientific Computing 57, no. 3 (June 25, 2013): 582–603. http://dx.doi.org/10.1007/s10915-013-9718-8.

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41

Hempert, F., M. Hoffmann, U. Iben, and C. D. Munz. "On the simulation of industrial gas dynamic applications with the discontinuous Galerkin spectral element method." Journal of Thermal Science 25, no. 3 (June 2016): 250–57. http://dx.doi.org/10.1007/s11630-016-0857-8.

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42

F. Antonietti, Paola, Francesco Bonaldi, and Ilario Mazzieri. "Simulation of three‐dimensional elastoacoustic wave propagation based on a Discontinuous Galerkin spectral element method." International Journal for Numerical Methods in Engineering 121, no. 10 (May 30, 2020): 2206–26. http://dx.doi.org/10.1002/nme.6305.

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43

Li, Yi, and Z. J. Wang. "An Optimized Correction Procedure via Reconstruction Formulation for Broadband Wave Computation." Communications in Computational Physics 13, no. 5 (May 2013): 1265–91. http://dx.doi.org/10.4208/cicp.300711.070512a.

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AbstractRecently, a new differential discontinuous formulation for conservation laws named the Correction Procedure via Reconstruction (CPR) is developed, which is in-spired by several other discontinuous methods such as the discontinuous Galerkin (DG), the spectral volume (SV)/spectral difference (SD) methods. All of them can be unified under the CPR formulation, which is relatively simple to implement due to its finite-difference-like framework. In this paper, a different discontinuous solution space including both polynomial and Fourier basis functions on each element is employed to compute broad-band waves. Free-parameters introduced in the Fourier bases are optimized to minimize both dispersion and dissipation errors through a wave propagation analysis. The optimization procedure is verified with a mesh resolution analysis. Numerical results are presented to demonstrate the performance of the optimized CPR formulation.

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44

CASTEL, N., G. COHEN, and M. DURUFLÉ. "APPLICATION OF DISCONTINUOUS GALERKIN SPECTRAL METHOD ON HEXAHEDRAL ELEMENTS FOR AEROACOUSTIC." Journal of Computational Acoustics 17, no. 02 (June 2009): 175–96. http://dx.doi.org/10.1142/s0218396x09003914.

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A discontinuous Galerkin method is developed for linear hyperbolic systems on general hexahedral meshes. The use of hexahedral elements and tensorized quadrature formulas to evaluate the integrals leads to an efficient matrix–vector product. It is shown that for high order approximations, the reduction in computational time can be very important, compared to tetrahedral elements. Two choices of quadrature points are considered, the Gauss points or Gauss–Lobatto points. The method is applied to the aeroacoustic system ("simplified" Linearized Euler Equations). Some 3D numerical experiments show the importance of penalization, and the advantage of using high order.

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45

Bohm, Marvin, Sven Schermeng, Andrew R. Winters, Gregor J. Gassner, and Gustaaf B. Jacobs. "Multi-element SIAC Filter for Shock Capturing Applied to High-Order Discontinuous Galerkin Spectral Element Methods." Journal of Scientific Computing 81, no. 2 (August 26, 2019): 820–44. http://dx.doi.org/10.1007/s10915-019-01036-8.

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46

Zeifang, Jonas, and Andrea Beck. "A data-driven high order sub-cell artificial viscosity for the discontinuous Galerkin spectral element method." Journal of Computational Physics 441 (September 2021): 110475. http://dx.doi.org/10.1016/j.jcp.2021.110475.

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47

Komperda, Jonathan, Zia Ghiasi, Dongru Li, Ahmad Peyvan, Farhad Jaberi, and Farzad Mashayek. "A hybrid discontinuous spectral element method and filtered mass density function solver for turbulent reacting flows." Numerical Heat Transfer, Part B: Fundamentals 78, no. 1 (April 17, 2020): 1–29. http://dx.doi.org/10.1080/10407790.2020.1746608.

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48

Bin, Jonghoon, William S. Oates, and M. Yousuff Hussaini. "An analysis of a discontinuous spectral element method for elastic wave propagation in a heterogeneous material." Computational Mechanics 55, no. 4 (March 6, 2015): 789–804. http://dx.doi.org/10.1007/s00466-015-1137-2.

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49

Gassner, Gregor J., Andrew R. Winters, and David A. Kopriva. "A well balanced and entropy conservative discontinuous Galerkin spectral element method for the shallow water equations." Applied Mathematics and Computation 272 (January 2016): 291–308. http://dx.doi.org/10.1016/j.amc.2015.07.014.

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Marras, Simone, James F. Kelly, Margarida Moragues, Andreas Müller, Michal A. Kopera, Mariano Vázquez, Francis X. Giraldo, Guillaume Houzeaux, and Oriol Jorba. "A Review of Element-Based Galerkin Methods for Numerical Weather Prediction: Finite Elements, Spectral Elements, and Discontinuous Galerkin." Archives of Computational Methods in Engineering 23, no. 4 (May 19, 2015): 673–722. http://dx.doi.org/10.1007/s11831-015-9152-1.

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