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Journal articles on the topic 'Advection-Dominated problems'

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Author: Grafiati

Published: 13 April 2024

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1

Abgrall, Rémi, and Arnaud Krust. "An adaptive enrichment algorithm for advection-dominated problems." International Journal for Numerical Methods in Fluids 72, no. 3 (November 9, 2012): 359–74. http://dx.doi.org/10.1002/fld.3745.

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2

Chen, Zhangxin, So-Hsiang Chou, and Do Young Kwak. "Characteristic-mixed covolume methods for advection-dominated diffusion problems." Numerical Linear Algebra with Applications 13, no. 9 (2006): 677–97. http://dx.doi.org/10.1002/nla.492.

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3

Park, Nam-Sik, and James A. Liggett. "Taylor-least-squares finite element for two-dimensional advection-dominated unsteady advection-diffusion problems." International Journal for Numerical Methods in Fluids 11, no. 1 (July 5, 1990): 21–38. http://dx.doi.org/10.1002/fld.1650110103.

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4

Lee, J. H. W., J. Peraire, and O. C. Zienkiewicz. "The characteristic-Galerkin method for advection-dominated problems—An assessment." Computer Methods in Applied Mechanics and Engineering 61, no. 3 (April 1987): 359–69. http://dx.doi.org/10.1016/0045-7825(87)90100-9.

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5

Brezzi, F., G. Gazzaniga, and L. D. Marini. "A preconditioner for domain decomposition methods for advection-dominated problems." Transport Theory and Statistical Physics 25, no. 3-5 (April 1996): 555–65. http://dx.doi.org/10.1080/00411459608220721.

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6

Chen, Zhangxin. "Characteristic-nonconforming finite-element methods for advection-dominated diffusion problems." Computers & Mathematics with Applications 48, no. 7-8 (October 2004): 1087–100. http://dx.doi.org/10.1016/j.camwa.2004.10.007.

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7

Lube, Gert, and Gerd Rapin. "Residual-based stabilized higher-order FEM for advection-dominated problems." Computer Methods in Applied Mechanics and Engineering 195, no. 33-36 (July 2006): 4124–38. http://dx.doi.org/10.1016/j.cma.2005.07.017.

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8

Pilatti, Cristiana, Bárbara Denicol do Amaral Rodriguez, and João Francisco Prolo Filho. "Performance Analysis of Stehfest and Power Series Expansion Methods for Solution to Diffusive and Advective Transport Problems." Defect and Diffusion Forum 396 (August 2019): 99–108. http://dx.doi.org/10.4028/www.scientific.net/ddf.396.99.

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This paper presents results of the test of methods for numerical inversion of the Laplace Transform for solving the one-dimensional advection-diffusion equation, which describes solute transport processes, focusing on the contaminant transport in a porous medium. The performance of Stehfest and Power Series Expansion methods is analyzed, for diffusion-dominated and advection-dominated transport problems under linear flow condition. Numerical results are compared to the analytical solution by means of the absolute error. Based on these results, we concluded that both methods, Stehfest and Power Series Expansion, are recommended only for diffusion-dominated cases.

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9

Shilt, Troy, Patrick J. O’Hara, and Jack J. McNamara. "Stabilization of advection dominated problems through a generalized finite element method." Computer Methods in Applied Mechanics and Engineering 383 (September 2021): 113889. http://dx.doi.org/10.1016/j.cma.2021.113889.

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10

Chen, Peng, Alfio Quarteroni, and Gianluigi Rozza. "Stochastic Optimal Robin Boundary Control Problems of Advection-Dominated Elliptic Equations." SIAM Journal on Numerical Analysis 51, no. 5 (January 2013): 2700–2722. http://dx.doi.org/10.1137/120884158.

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11

Chen, Zhangxin. "Characteristic mixed discontinuous finite element methods for advection-dominated diffusion problems." Computer Methods in Applied Mechanics and Engineering 191, no. 23-24 (March 2002): 2509–38. http://dx.doi.org/10.1016/s0045-7825(01)00411-x.

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12

Arbogast, Todd, and Mary F. Wheeler. "A Characteristics-Mixed Finite Element Method for Advection-Dominated Transport Problems." SIAM Journal on Numerical Analysis 32, no. 2 (April 1995): 404–24. http://dx.doi.org/10.1137/0732017.

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13

Bris, Claude Le, Frédéric Legoll, and François Madiot. "Multiscale Finite Element Methods for Advection-Dominated Problems in Perforated Domains." Multiscale Modeling & Simulation 17, no. 2 (January 2019): 773–825. http://dx.doi.org/10.1137/17m1152048.

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14

Wheeler, Mary Fanett, Wendy A. Kinton, and Clint N. Dawson. "Time-splitting for advection-dominated parabolic problems in one space variable." Communications in Applied Numerical Methods 4, no. 3 (May 1988): 413–23. http://dx.doi.org/10.1002/cnm.1630040316.

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15

Huang, Tsung-Hui. "Stabilized and variationally consistent integrated meshfree formulation for advection-dominated problems." Computer Methods in Applied Mechanics and Engineering 403 (January 2023): 115698. http://dx.doi.org/10.1016/j.cma.2022.115698.

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16

Ahmadi, Hossein. "A numerical scheme for advection dominated problems based on a Lagrange interpolation." Groundwater for Sustainable Development 13 (May 2021): 100542. http://dx.doi.org/10.1016/j.gsd.2020.100542.

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17

El-Amrani, Mofdi, Abdellah El Kacimi, Bassou Khouya, and Mohammed Seaid. "A Bernstein–Bézier Lagrange–Galerkin method for three-dimensional advection-dominated problems." Computer Methods in Applied Mechanics and Engineering 403 (January 2023): 115758. http://dx.doi.org/10.1016/j.cma.2022.115758.

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18

Sacco, Riccardo. "Exponentially fitted shape functions for advection-dominated flow problems in two dimensions." Journal of Computational and Applied Mathematics 67, no. 1 (February 1996): 161–65. http://dx.doi.org/10.1016/0377-0427(95)00149-2.

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19

Bartlett, Roscoe A., Matthias Heinkenschloss, Denis Ridzal, and Bart G. van Bloemen Waanders. "Domain decomposition methods for advection dominated linear-quadratic elliptic optimal control problems." Computer Methods in Applied Mechanics and Engineering 195, no. 44-47 (September 2006): 6428–47. http://dx.doi.org/10.1016/j.cma.2006.01.009.

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20

Kubatko, Ethan J., Joannes J. Westerink, and Clint Dawson. "hp Discontinuous Galerkin methods for advection dominated problems in shallow water flow." Computer Methods in Applied Mechanics and Engineering 196, no. 1-3 (December 2006): 437–51. http://dx.doi.org/10.1016/j.cma.2006.05.002.

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21

Manzini, Gianmarco, and Alessandro Russo. "A finite volume method for advection–diffusion problems in convection-dominated regimes." Computer Methods in Applied Mechanics and Engineering 197, no. 13-16 (February 2008): 1242–61. http://dx.doi.org/10.1016/j.cma.2007.11.014.

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22

Hindmarsh, Alan C. "Avoiding BDF stability barriers in the MOL solution of advection-dominated problems." Applied Numerical Mathematics 17, no. 3 (July 1995): 311–18. http://dx.doi.org/10.1016/0168-9274(95)00036-t.

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23

Ruan, Feng, and Dennis McLaughlin. "An investigation of Eulerian-Lagrangian Methods for solving heterogeneous advection-dominated transport problems." Water Resources Research 35, no. 8 (August 1999): 2359–73. http://dx.doi.org/10.1029/1999wr900049.

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24

Brezzi, F., L. D. Marini, S. Micheletti, P. Pietra, and R. Sacco. "Stability and error analysis of mixed finite-volume methods for advection dominated problems." Computers & Mathematics with Applications 51, no. 5 (March 2006): 681–96. http://dx.doi.org/10.1016/j.camwa.2006.03.001.

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25

Torlo, Davide, Francesco Ballarin, and Gianluigi Rozza. "Stabilized Weighted Reduced Basis Methods for Parametrized Advection Dominated Problems with Random Inputs." SIAM/ASA Journal on Uncertainty Quantification 6, no. 4 (January 2018): 1475–502. http://dx.doi.org/10.1137/17m1163517.

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26

RUSSO, ALESSANDRO. "A POSTERIORI ERROR ESTIMATORS VIA BUBBLE FUNCTIONS." Mathematical Models and Methods in Applied Sciences 06, no. 01 (February 1996): 33–41. http://dx.doi.org/10.1142/s0218202596000031.

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In this paper we discuss a way to recover a classical residual-based error estimator for elliptic problems by using a finite element space enriched with bubble functions. The advection-dominated case is also discussed.

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27

Hadadian Nejad Yousefi, Mohsen, Seyed Hossein Ghoreishi Najafabadi, and Emran Tohidi. "A new spectral integral equation method for solving two-dimensional unsteady advection-diffusion equations via Chebyshev polynomials." Engineering Computations 36, no. 7 (August 12, 2019): 2327–68. http://dx.doi.org/10.1108/ec-02-2018-0063.

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Purpose The purpose of this paper is to develop an efficient and reliable spectral integral equation method for solving two-dimensional unsteady advection-diffusion equations. Design/methodology/approach In this study, the considered two-dimensional unsteady advection-diffusion equations are transformed into the equivalent partial integro-differential equations via integrating from the considered unsteady advection-diffusion equation. After this stage, by using Chebyshev polynomials of the first kind and the operational matrix of integration, the integral equation would be transformed into the system of linear algebraic equations. Robustness and efficiency of the proposed method were illustrated by six numerical simulations experimentally. The numerical results confirm that the method is efficient, highly accurate, fast and stable for solving two-dimensional unsteady advection-diffusion equations. Findings The proposed method can solve the equations with discontinuity near the boundaries, the advection-dominated equations and the equations in irregular domains. One of the numerical test problems designed specially to evaluate the performance of the proposed method for discontinuity near boundaries. Originality/value This study extends the intention of one dimensional Chebyshev approximate approaches (Yuksel and Sezer, 2013; Yuksel et al., 2015) for two-dimensional unsteady advection-diffusion problems and the basic intention of our suggested method is quite different from the approaches for hyperbolic problems (Bulbul and Sezer, 2011).

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28

Tassi, Tommaso, Alberto Zingaro, and Luca Dede'. "A machine learning approach to enhance the SUPG stabilization method for advection-dominated differential problems." Mathematics in Engineering 5, no. 2 (2022): 1–26. http://dx.doi.org/10.3934/mine.2023032.

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<abstract><p>We propose using machine learning and artificial neural networks (ANNs) to enhance residual-based stabilization methods for advection-dominated differential problems. Specifically, in the context of the finite element method, we consider the streamline upwind Petrov-Galerkin (SUPG) stabilization method and we employ ANNs to optimally choose the stabilization parameter on which the method relies. We generate our dataset by solving optimization problems to find the optimal stabilization parameters that minimize the distances among the numerical and the exact solutions for different data of differential problem and the numerical settings of the finite element method, e.g., mesh size and polynomial degree. The dataset generated is used to train the ANN, and we used the latter "online" to predict the optimal stabilization parameter to be used in the SUPG method for any given numerical setting and problem data. We show, by means of 1D and 2D numerical tests for the advection-dominated differential problem, that our ANN approach yields more accurate solution than using the conventional stabilization parameter for the SUPG method.</p></abstract>

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29

Borio, Andrea, Martina Busetto, and Francesca Marcon. "SUPG-stabilized stabilization-free VEM: a numerical investigation." Mathematics in Engineering 6, no. 1 (2024): 173–91. http://dx.doi.org/10.3934/mine.2024008.

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<abstract><p>We numerically investigate the possibility of defining Stabilization-Free Virtual Element discretizations–i.e., Virtual Element Method discretizations without an additional non-polynomial non-operator-preserving stabilization term–of advection-diffusion problems in the advection-dominated regime, considering a Streamline Upwind Petrov-Galerkin stabilized formulation of the scheme. We present numerical tests that assess the robustness of the proposed scheme and compare it with a standard Virtual Element Method.</p></abstract>

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30

Nicolini, Julio L., and Fernando L. Teixeira. "Reduced-Order Modeling of Advection-Dominated Kinetic Plasma Problems by Shifted Proper Orthogonal Decomposition." IEEE Transactions on Plasma Science 49, no. 11 (November 2021): 3689–99. http://dx.doi.org/10.1109/tps.2021.3115657.

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31

Nicolini, Julio L., and Fernando L. Teixeira. "Reduced-Order Modeling of Advection-Dominated Kinetic Plasma Problems by Shifted Proper Orthogonal Decomposition." IEEE Transactions on Plasma Science 49, no. 11 (November 2021): 3689–99. http://dx.doi.org/10.1109/tps.2021.3115657.

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32

Solán-Fustero, P., J. L. Gracia, A. Navas-Montilla, and P. García-Navarro. "A POD-based ROM strategy for the prediction in time of advection-dominated problems." Journal of Computational Physics 471 (December 2022): 111672. http://dx.doi.org/10.1016/j.jcp.2022.111672.

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33

Burman, Erik. "Robust error estimates in weak norms for advection dominated transport problems with rough data." Mathematical Models and Methods in Applied Sciences 24, no. 13 (September 17, 2014): 2663–84. http://dx.doi.org/10.1142/s021820251450033x.

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We consider transient convection–diffusion equations with a velocity vector field with multiscale character and rough data. We assume that the velocity field has two scales, a coarse scale with slow spatial variation, which is responsible for advective transport and a fine scale with small amplitude that contributes to the mixing. For this problem we consider the estimation of filtered error quantities for solutions computed using a finite element method with symmetric stabilization. A posteriori error estimates and a priori error estimates are derived using the multiscale decomposition of the advective velocity to improve stability. All estimates are independent both of the Péclet number and of the regularity of the exact solution.

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34

Mavrič, Boštjan, and Božidar Šarler. "Equivalent-PDE based stabilization of strong-form meshless methods applied to advection-dominated problems." Engineering Analysis with Boundary Elements 113 (April 2020): 315–27. http://dx.doi.org/10.1016/j.enganabound.2020.01.014.

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35

Lombardi, Ariel L., Paola Pietra, and Mariana I. Prieto. "A posteriori error estimator for exponentially fitted Discontinuous Galerkin approximation of advection dominated problems." Calcolo 53, no. 1 (February 24, 2015): 83–103. http://dx.doi.org/10.1007/s10092-015-0138-z.

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36

Pinelli, A., W. Couzy, M. O. Deville, and C. Benocci. "An Efficient Iterative Solution Method for the Chebyshev Collocation of Advection-Dominated Transport Problems." SIAM Journal on Scientific Computing 17, no. 3 (May 1996): 647–57. http://dx.doi.org/10.1137/s1064827593253835.

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37

Corekli, Cagnur. "The SIPG method of Dirichlet boundary optimal control problems with weakly imposed boundary conditions." AIMS Mathematics 7, no. 4 (2022): 6711–42. http://dx.doi.org/10.3934/math.2022375.

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<abstract><p>In this paper, we consider the symmetric interior penalty Galerkin (SIPG) method which is one of Discontinuous Galerkin Methods for the Dirichlet optimal control problems governed by linear advection-diffusion-reaction equation on a convex polygonal domain and the difficulties which we faced while solving this problem numerically. Since standard Galerkin methods have failed when the boundary layers have occurred and advection diffusion has dominated, these difficulties can occur in the cases of higher order elements and non smooth Dirichlet data in using standard finite elements. We find the most convenient natural setting of Dirichlet boundary control problem for the Laplacian and the advection diffusion reaction equations.After converting the continuous problem to an optimization problem, we solve it by "discretize-then-optimize" approach. In final, we estimate the optimal priori error estimates in suitable norms of the solutions and then support the result and the features of the method with numerical examples on the different kinds of domain.</p></abstract>

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38

Lasota, J. P. "Models of Soft X-Ray Transients and Dwarf Novae." International Astronomical Union Colloquium 158 (1996): 385–94. http://dx.doi.org/10.1017/s0252921100039221.

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AbstractModels of Soft X-ray Transients are presented and compared with observations. The importance of inner advection-dominated flows in quiescent transient sources is discussed, as well as the problem of global stability of the standard outer accretion disc. A comparison is made with similar problems in dwarf nova models.

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39

Dutta, Sourav, Peter Rivera-Casillas, Brent Styles, and Matthew W. Farthing. "Reduced Order Modeling Using Advection-Aware Autoencoders." Mathematical and Computational Applications 27, no. 3 (April 21, 2022): 34. http://dx.doi.org/10.3390/mca27030034.

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Physical systems governed by advection-dominated partial differential equations (PDEs) are found in applications ranging from engineering design to weather forecasting. They are known to pose severe challenges to both projection-based and non-intrusive reduced order modeling, especially when linear subspace approximations are used. In this work, we develop an advection-aware (AA) autoencoder network that can address some of these limitations by learning efficient, physics-informed, nonlinear embeddings of the high-fidelity system snapshots. A fully non-intrusive reduced order model is developed by mapping the high-fidelity snapshots to a latent space defined by an AA autoencoder, followed by learning the latent space dynamics using a long-short-term memory (LSTM) network. This framework is also extended to parametric problems by explicitly incorporating parameter information into both the high-fidelity snapshots and the encoded latent space. Numerical results obtained with parametric linear and nonlinear advection problems indicate that the proposed framework can reproduce the dominant flow features even for unseen parameter values.

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40

Heinkenschloss, Matthias, and Dmitriy Leykekhman. "Local Error Estimates for SUPG Solutions of Advection-Dominated Elliptic Linear-Quadratic Optimal Control Problems." SIAM Journal on Numerical Analysis 47, no. 6 (January 2010): 4607–38. http://dx.doi.org/10.1137/090759902.

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41

Calo, V. M., M. Łoś, Q. Deng, I. Muga, and M. Paszyński. "Isogeometric Residual Minimization Method (iGRM) with direction splitting preconditioner for stationary advection-dominated diffusion problems." Computer Methods in Applied Mechanics and Engineering 373 (January 2021): 113214. http://dx.doi.org/10.1016/j.cma.2020.113214.

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42

Maday, Yvon, Andrea Manzoni, and Alfio Quarteroni. "An online intrinsic stabilization strategy for the reduced basis approximation of parametrized advection-dominated problems." Comptes Rendus Mathematique 354, no. 12 (December 2016): 1188–94. http://dx.doi.org/10.1016/j.crma.2016.10.008.

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43

Haugen, Joakim, and Lars Imsland. "Monitoring an Advection-Diffusion Process Using Aerial Mobile Sensors." Unmanned Systems 03, no. 03 (July 2015): 221–38. http://dx.doi.org/10.1142/s2301385015500144.

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A path planning framework for regional surveillance of a planar advection-diffusion process by aerial mobile sensors is proposed. The goal of the path planning is to produce feasible and collision-free trajectories for a set of aerial mobile sensors that minimize some uncertainty measure of the process under observation. The problem is formulated as a dynamic optimization problem and discretized into a large-scale nonlinear programming (NLP) problem using the Petrov–Galerkin finite element method in space and simultaneous collocation in time. Receding horizon optimization problems are solved in simulations with an advection-dominated ice concentration field. Simulations illustrate the usefulness of the proposed method.

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44

Giraldo, Juan F., and Victor M. Calo. "An Adaptive in Space, Stabilized Finite Element Method via Residual Minimization for Linear and Nonlinear Unsteady Advection–Diffusion–Reaction Equations." Mathematical and Computational Applications 28, no. 1 (January 6, 2023): 7. http://dx.doi.org/10.3390/mca28010007.

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We construct a stabilized finite element method for linear and nonlinear unsteady advection–diffusion–reaction equations using the method of lines. We propose a residual minimization strategy that uses an ad-hoc modified discrete system that couples a time-marching schema and a semi-discrete discontinuous Galerkin formulation in space. This combination delivers a stable continuous solution and an on-the-fly error estimate that robustly guides adaptivity at every discrete time. We show the performance of advection-dominated problems to demonstrate stability in the solution and efficiency in the adaptivity strategy. We also present the method’s robustness in the nonlinear Bratu equation in two dimensions.

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45

Sangalli, Giancarlo. "Global and Local Error Analysis for the Residual-Free Bubbles Method Applied to Advection-Dominated Problems." SIAM Journal on Numerical Analysis 38, no. 5 (January 2000): 1496–522. http://dx.doi.org/10.1137/s0036142999365382.

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46

Le Bris, Claude, Frédéric Legoll, and François Madiot. "A numerical comparison of some Multiscale Finite Element approaches for advection-dominated problems in heterogeneous media." ESAIM: Mathematical Modelling and Numerical Analysis 51, no. 3 (April 5, 2017): 851–88. http://dx.doi.org/10.1051/m2an/2016057.

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47

Leykekhman, Dmitriy, and Matthias Heinkenschloss. "Local Error Analysis of Discontinuous Galerkin Methods for Advection-Dominated Elliptic Linear-Quadratic Optimal Control Problems." SIAM Journal on Numerical Analysis 50, no. 4 (January 2012): 2012–38. http://dx.doi.org/10.1137/110826953.

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48

Kempka, Thomas. "Verification of a Python-based TRANsport Simulation Environment for density-driven fluid flow and coupled transport of heat and chemical species." Advances in Geosciences 54 (October 14, 2020): 67–77. http://dx.doi.org/10.5194/adgeo-54-67-2020.

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Abstract. Numerical simulation has become an inevitable tool for improving the understanding on coupled processes in the geological subsurface and its utilisation. However, most of the available open source and commercial modelling codes do not come with flexible chemical modules or simply do not offer a straight-forward way to couple third-party chemical libraries. For that reason, the simple and efficient TRANsport Simulation Environment (TRANSE) has been developed based on the Finite Difference Method in order to solve the density-driven formulation of the Darcy flow equation, coupled with the equations for transport of heat and chemical species. Simple explicit, weighted semi-implicit or fully-implicit numerical schemes are available for the solution of the system of partial differential equations, whereby the entire numerical code is composed of less than 1000 lines of Python code, only. A diffusive flux-corrected advection scheme can be employed in addition to pure upwinding to minimise numerical diffusion in advection-dominated transport problems. The objective of the present study is to verify the numerical code implementation by means of benchmarks for density-driven fluid flow and advection-dominated transport. In summary, TRANSE exhibits a very good agreement with established numerical simulation codes for the benchmarks investigated here. Consequently, its applicability to numerical density-driven flow and transport problems is proven. The main advantage of the presented numerical code is that the implementation of complex problem-specific couplings between flow, transport and chemical reactions becomes feasible without substantial investments in code development using a low-level programming language, but the easy-to-read and -learn Python programming language.

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49

Chen, Huanzhen, Lei Gao, and Hong Wang. "Uniform estimates for characteristics-mixed finite method for transient advection-dominated diffusion problems in two-dimensional space." Applied Mathematics and Computation 280 (April 2016): 86–102. http://dx.doi.org/10.1016/j.amc.2016.01.031.

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50

CHACÓN REBOLLO, TOMÁS, MACARENA GÓMEZ MÁRMOL, and GLADYS NARBONA REINA. "NUMERICAL ANALYSIS OF THE PSI SOLUTION OF ADVECTION–DIFFUSION PROBLEMS THROUGH A PETROV–GALERKIN FORMULATION." Mathematical Models and Methods in Applied Sciences 17, no. 11 (November 2007): 1905–36. http://dx.doi.org/10.1142/s0218202507002510.

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In this paper we introduce an analysis technique for the solution of the steady advection–diffusion equation by the PSI (Positive Streamwise Implicit) method. We formulate this approximation as a nonlinear finite element Petrov–Galerkin scheme, and use tools of functional analysis to perform a convergence, error and maximum principle analysis. We prove that the scheme is first-order accurate in H1 norm, and well-balanced up to second order for convection-dominated flows. We give some numerical evidence that the scheme is only first-order accurate in L2 norm. Our analysis also holds for other nonlinear Fluctuation Splitting schemes that can be built from first-order monotone schemes by the Abgrall and Mezine's technique.

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