Academic literature on the topic 'High-Order finite element methods'
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Journal articles on the topic "High-Order finite element methods":
Abreu, Eduardo, Ciro Díaz, Juan Galvis, and Marcus Sarkis. "On high-order conservative finite element methods." Computers & Mathematics with Applications 75, no. 6 (March 2018): 1852–67. http://dx.doi.org/10.1016/j.camwa.2017.10.020.
Harari, Isaac, and Danny Avraham. "High-Order Finite Element Methods for Acoustic Problems." Journal of Computational Acoustics 05, no. 01 (March 1997): 33–51. http://dx.doi.org/10.1142/s0218396x97000046.
Bagheri, Babak, L. Ridgway Scott, and Shangyou Zhang. "Implementing and using high-order finite element methods." Finite Elements in Analysis and Design 16, no. 3-4 (June 1994): 175–89. http://dx.doi.org/10.1016/0168-874x(94)90063-9.
Lin, Qun, and Junming Zhou. "Superconvergence in high-order Galerkin finite element methods." Computer Methods in Applied Mechanics and Engineering 196, no. 37-40 (August 2007): 3779–84. http://dx.doi.org/10.1016/j.cma.2006.10.027.
Larson, Mats G., and Sara Zahedi. "Stabilization of high order cut finite element methods on surfaces." IMA Journal of Numerical Analysis 40, no. 3 (April 25, 2019): 1702–45. http://dx.doi.org/10.1093/imanum/drz021.
Winther, Kaibo Hu &. Ragnar. "Well-Conditioned Frames for High Order Finite Element Methods." Journal of Computational Mathematics 39, no. 3 (June 2021): 333–57. http://dx.doi.org/10.4208/jcm.2001-m2018-0078.
Dobrev, Veselin A., Tzanio V. Kolev, and Robert N. Rieben. "High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics." SIAM Journal on Scientific Computing 34, no. 5 (January 2012): B606—B641. http://dx.doi.org/10.1137/120864672.
Yurun, Fan, and M. J. Crochet. "High-order finite element methods for steady viscoelastic flows." Journal of Non-Newtonian Fluid Mechanics 57, no. 2-3 (May 1995): 283–311. http://dx.doi.org/10.1016/0377-0257(94)01338-i.
Opschoor, Joost A. A., Philipp C. Petersen, and Christoph Schwab. "Deep ReLU networks and high-order finite element methods." Analysis and Applications 18, no. 05 (February 21, 2020): 715–70. http://dx.doi.org/10.1142/s0219530519410136.
Jund, Sébastien, and Stéphanie Salmon. "Arbitrary High-Order Finite Element Schemes and High-Order Mass Lumping." International Journal of Applied Mathematics and Computer Science 17, no. 3 (October 1, 2007): 375–93. http://dx.doi.org/10.2478/v10006-007-0031-2.
Dissertations / Theses on the topic "High-Order finite element methods":
Marais, Neilen. "Efficient high-order time domain finite element methods in electromagnetics." Thesis, Stellenbosch : University of Stellenbosch, 2009. http://hdl.handle.net/10019.1/1499.
The Finite Element Method (FEM) as applied to Computational Electromagnetics (CEM), can beused to solve a large class of Electromagnetics problems with high accuracy and good computational efficiency. For solving wide-band problems time domain solutions are often preferred; while time domain FEM methods are feasible, the Finite Difference Time Domain (FDTD) method is more commonly applied. The FDTD is popular both for its efficiency and its simplicity. The efficiency of the FDTD stems from the fact that it is both explicit (i.e. no matrices need to be solved) and second order accurate in both time and space. The FDTD has limitations when dealing with certain geometrical shapes and when electrically large structures are analysed. The former limitation is caused by stair-casing in the geometrical modelling, the latter by accumulated dispersion error throughout the mesh. The FEM can be seen as a general mathematical framework describing families of concrete numerical method implementations; in fact the FDTD can be described as a particular FETD (Finite Element Time Domain) method. To date the most commonly described FETD CEM methods make use of unstructured, conforming meshes and implicit time stepping schemes. Such meshes deal well with complex geometries while implicit time stepping is required for practical numerical stability. Compared to the FDTD, these methods have the advantages of computational efficiency when dealing with complex geometries and the conceptually straight forward extension to higher orders of accuracy. On the downside, they are much more complicated to implement and less computationally efficient when dealing with regular geometries. The FDTD and implicit FETD have been combined in an implicit/explicit hybrid. By using the implicit FETD in regions of complex geometry and the FDTD elsewhere the advantages of both are combined. However, previous work only addressed mixed first order (i.e. second order accurate) methods. For electrically large problems or when very accurate solutions are required, higher order methods are attractive. In this thesis a novel higher order implicit/explicit FETD method of arbitrary order in space is presented. A higher order explicit FETD method is implemented using Gauss-Lobatto lumping on regular Cartesian hexahedra with central differencing in time applied to a coupled Maxwell’s equation FEM formulation. This can be seen as a spatially higher order generalisation of the FDTD. A convolution-free perfectly matched layer (PML) method is adapted from the FDTD literature to provide mesh termination. A curl conforming hybrid mesh allowing the interconnection of arbitrary order tetrahedra and hexahedra without using intermediate pyramidal or prismatic elements is presented. An unconditionally stable implicit FETD method is implemented using Newmark-Beta time integration and the standard curl-curl FEM formulation. The implicit/explicit hybrid is constructed on the hybrid hexahedral/tetrahedral mesh using the equivalence between the coupled Maxwell’s formulation with central differences and the Newmark-Beta method with Beta = 0 and the element-wise implicitness method. The accuracy and efficiency of this hybrid is numerically demonstrated using several test-problems.
Franke, David [Verfasser]. "Investigation of mechanical contact problems with high-order Finite Element Methods / David Franke." Aachen : Shaker, 2012. http://d-nb.info/1067734902/34.
Al-Shanfari, Fatima. "High-order in time discontinuous Galerkin finite element methods for linear wave equations." Thesis, Brunel University, 2017. http://bura.brunel.ac.uk/handle/2438/15332.
Marrett, Sean 1960. "A high-order finite element method for Tokamak plasma equilibria /." Thesis, McGill University, 1992. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=56809.
Moura, Rodrigo Costa. "A high-order unstructured discontinuous galerkin finite element method for aerodynamics." Instituto Tecnológico de Aeronáutica, 2012. http://www.bd.bibl.ita.br/tde_busca/arquivo.php?codArquivo=2158.
Guo, Ruchi. "Design, Analysis, and Application of Immersed Finite Element Methods." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/90374.
Doctor of Philosophy
Interface problems arise from many science and engineering applications modeling the transmission of some physical quantities between multiple materials. Mathematically, these multiple materials in general are modeled by partial differential equations (PDEs) with discontinuous parameters, which poses challenges to developing efficient and reliable numerical methods and the related theoretical error analysis. The main contributions of this dissertation is on the development of a special finite element method, the so called immersed finite element (IFE) method, to solve the interface problems on a mesh independent of the interface geometry which can be advantageous especially when the interface is moving. Specifically, this dissertation consists of three projects of IFE methods: elasticity interface problems, higher-order IFE methods and interface inverse problems, including their design, analysis, and application.
Chuang, Shih-Chang. "Parallel methods for high-performance finite element methods based on sparsity." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/18177.
Zhou, Dong. "High-order numerical methods for pressure Poisson equation reformulations of the incompressible Navier-Stokes equations." Diss., Temple University Libraries, 2014. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/295839.
Ph.D.
Projection methods for the incompressible Navier-Stokes equations (NSE) are efficient, but introduce numerical boundary layers and have limited temporal accuracy due to their fractional step nature. The Pressure Poisson Equation (PPE) reformulations represent a class of methods that replace the incompressibility constraint by a Poisson equation for the pressure, with a suitable choice of the boundary condition so that the incompressibility is maintained. PPE reformulations of the NSE have important advantages: the pressure is no longer implicitly coupled to the velocity, thus can be directly recovered by solving a Poisson equation, and no numerical boundary layers are generated; arbitrary order time-stepping schemes can be used to achieve high order accuracy in time. In this thesis, we focus on numerical approaches of the PPE reformulations, in particular, the Shirokoff-Rosales (SR) PPE reformulation. Interestingly, the electric boundary conditions, i.e., the tangential and divergence boundary conditions, provided for the velocity in the SR PPE reformulation render classical nodal finite elements non-convergent. We propose two alternative methodologies, mixed finite element methods and meshfree finite differences, and demonstrate that these approaches allow for arbitrary order of accuracy both in space and in time.
Temple University--Theses
Couchman, Benjamin Luke Streatfield. "On the convergence of higher-order finite element methods to weak solutions." Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/115685.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 77-79).
The ability to handle discontinuities appropriately is essential when solving nonlinear hyperbolic partial differential equations (PDEs). Discrete solutions to the PDE must converge to weak solutions in order for the discontinuity propagation speed to be correct. As shown by the Lax-Wendroff theorem, one method to guarantee that convergence, if it occurs, will be to a weak solution is to use a discretely conservative scheme. However, discrete conservation is not a strict requirement for convergence to a weak solution. This suggests a hierarchy of discretizations, where discretely conservative schemes are a subset of the larger class of methods that converge to the weak solution. We show here that a range of finite element methods converge to the weak solution without using discrete conservation arguments. The effect of using quadrature rules to approximate integrals is also considered. In addition, we show that solutions using non-conservation working variables also converge to weak solutions.
by Benjamin Luke Streatfield Couchman.
S.M.
Sevilla, Cárdenas Rubén. "NURBS-Enhanced Finite Element Method (NEFEM)." Doctoral thesis, Universitat Politècnica de Catalunya, 2009. http://hdl.handle.net/10803/5857.
La implementació i aplicació de NEFEM a problemes que requereixen una descripció acurada del contorn són, també, objectius prioritaris d'aquesta tesi. Per exemple, la solució numèrica de les equacions de Maxwell és molt sensible a la descripció geomètrica. Es presenta l'aplicació de NEFEM a problemes d'scattering d'ones electromagnètiques amb una formulació de Galerkin discontinu. S'investiga l'habilitat de NEFEM per obtenir solucions precises amb malles grolleres i aproximacions d'alt ordre, i s'exploren les possibilitats de les anomenades malles NEFEM, amb elements que contenen singularitats dintre d'una cara o aresta d'un element. Utilitzant NEFEM, la mida de la malla no està controlada per la complexitat de la geometria. Això implica una dràstica diferència en la mida dels elements i, per tant, suposa un gran estalvi tant des del punt de vista de requeriments de memòria com de cost computacional. Per tant, NEFEM és una eina poderosa per la simulació de problemes tridimensionals a gran escala amb geometries complexes. D'altra banda, la simulació de problemes d'scattering d'ones electromagnètiques requereix mecanismes per aconseguir una absorció eficient de les ones scattered. En aquesta tesi es discuteixen, optimitzen i comparen dues tècniques en el context de mètodes de Galerkin discontinu amb aproximacions d'alt ordre.
La resolució numèrica de les equacions d'Euler de la dinàmica de gasos és també molt sensible a la representació geomètrica. Quan es considera una formulació de Galerkin discontinu i elements isoparamètrics lineals, una producció espúria d'entropia pot evitar la convergència cap a la solució correcta. Amb NEFEM, l'acurada imposició de la condició de contorn en contorns impenetrables proporciona resultats precisos inclús amb una aproximació lineal de la solució. A més, la representació exacta del contorn permet una imposició adequada de les condicions de contorn amb malles grolleres i graus d'interpolació alts. Una propietat atractiva de la implementació proposada és que moltes de les rutines usuals en un codi d'elements finits poden ser aprofitades, per exemple rutines per realitzar el càlcul de les matrius elementals, assemblatge, etc. Només és necessari implementar noves rutines per calcular les quadratures numèriques en elements corbs i emmagatzemar el valor de les funciones de forma en els punts d'integració. S'han proposat vàries tècniques d'elements finits corbs a la literatura. En aquesta tesi, es compara NEFEM amb altres tècniques populars d'elements finits corbs (isoparamètics, cartesians i p-FEM), des de tres punts de vista diferents: aspectes teòrics, implementació i eficiència numèrica. En els exemples numèrics, NEFEM és, com a mínim, un ordre de magnitud més precís comparat amb altres tècniques. A més, per una precisió desitjada NEFEM és també més eficient: necessita un 50% dels graus de llibertat que fan servir els elements isoparamètrics o p-FEM per aconseguir la mateixa precisió. Per tant, l'ús de NEFEM és altament recomanable en presència de contorns corbs i/o quan el contorn té detalls geomètrics complexes.
This thesis proposes an improvement of the classical finite element method (FEM) for an efficient treatment of curved boundaries: the NURBSenhanced FEM (NEFEM). It is able to exactly represent the geometry by means of the usual CAD boundary representation with non-uniform rational Bsplines (NURBS), while the solution is approximated with a standard piecewise polynomial interpolation. Therefore, in the vast majority of the domain, interpolation and numerical integration are standard, preserving the classical finite element (FE) convergence properties, and allowing a seamless coupling with standard FEs on the domain interior. Specifically designed polynomial interpolation and numerical integration are designed only for those elements affected by the NURBS boundary representation.
The implementation and application of NEFEM to problems demanding an accurate boundary representation are also primary goals of this thesis. For instance, the numerical solution of Maxwell's equations is highly sensitive to geometry description. The application of NEFEM to electromagnetic scattering problems using a discontinuous Galerkin formulation is presented. The ability of NEFEM to compute an accurate solution with coarse meshes and high-order approximations is investigated, and the possibilities of NEFEM meshes, with elements containing edge or corner singularities, are explored. With NEFEM, the mesh size is no longer subsidiary to geometry complexity, and depends only on the accuracy requirements on the solution, whereas standard FEs require mesh refinement to properly capture the geometry. This implies a drastic difference in mesh size that results in drastic memory savings, and also important savings in computational cost. Thus, NEFEM is a powerful tool for large-scale scattering simulations with complex geometries in three dimensions. Another key issue in the numerical solution of electromagnetic scattering problems is using a mechanism to perform the absorption of outgoing waves. Two perfectly matched layers are discussed, optimized and compared in a high-order discontinuous Galerkin framework.
The numerical solution of Euler equations of gas dynamics is also very sensitive to geometry description. Using a discontinuous Galerkin formulation and linear isoparametric elements, a spurious entropy production may prevent convergence to the correct solution. With NEFEM, the exact imposition of the solid wall boundary condition provides accurate results even with a linear approximation of the solution. Furthermore, the exact boundary representation allows using coarse meshes, but ensuring the proper implementation of the solid wall boundary condition. An attractive feature of the proposed implementation is that the usual routines of a standard FE code can be directly used, namely routines for the computation of elemental matrices and vectors, assembly, etc. It is only necessary to implement new routines for the computation of numerical quadratures in curved elements and to store the value of shape functions at integration points.
Several curved FE techniques have been proposed in the literature. In this thesis, NEFEM is compared with some popular curved FE techniques (namely isoparametric FEs, cartesian FEs and p-FEM), from three different perspectives: theoretical aspects, implementation and performance. In every example shown, NEFEM is at least one order of magnitude more accurate compared to other techniques. Moreover, for a desired accuracy NEFEM is also computationally more efficient. In some examples, NEFEM needs only 50% of the number of degrees of freedom required by isoparametric FEs or p-FEM. Thus, the use of NEFEM is strongly recommended in the presence of curved boundaries and/or when the boundary of the domain has complex geometric details.
Books on the topic "High-Order finite element methods":
S̆olin, Pavel. Higher-order finite element methods. Boca Raton, Fla: Chapman & Hall/CRC, 2004.
Vandandoo, Ulziibayar, Tugal Zhanlav, Ochbadrakh Chuluunbaatar, Alexander Gusev, Sergue Vinitsky, and Galmandakh Chuluunbaatar. High-Order Finite Difference and Finite Element Methods for Solving Some Partial Differential Equations. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-44784-6.
University of Wales. Institute for Numerical Methods in Engineering. and Langley Research Center. Aerothermal Loads Branch., eds. Finite element methods of analysis for high speed viscous flows. Hampton, Va: Aerothermal Loads Branch, Loads and Aeroelasticity Division, NASA Langley Research Center, 1987.
George C. Marshall Space Flight Center., ed. Velocity-pressure integrated versus penalty finite element methods for high Reynolds number flows. Marshall Space Flight Center, Ala: NASA-Marshall Space Flight Center, 1988.
George C. Marshall Space Flight Center., ed. Velocity-pressure integrated versus penalty finite element methods for high Reynolds number flows. Marshall Space Flight Center, Ala: NASA-Marshall Space Flight Center, 1988.
Zhang, Yong-Tao. High order WENO schemes for Hamilton-Jacobi equations on triangular meshes. Hampton, Va: ICASE, NASA Langley Research Center, 2001.
Yan, Jue. Local discontinuous Galerkin methods for partial differential equations with higher order derivates. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 2002.
Hsing-jen, Chang, and Langley Research Center, eds. H-P adaptive methods for finite element analysis of aerothermal loads in high-speed flows. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1993.
Xingren, Zhang, and Langley Research Center, eds. H-P adaptive methods for finite element analysis of aerothermal loads in high-speed flows. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1993.
Hsing-jen, Chang, and Langley Research Center, eds. H-P adaptive methods for finite element analysis of aerothermal loads in high-speed flows. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1993.
Book chapters on the topic "High-Order finite element methods":
Lyu, Yongtao. "High Order Lagrange Element." In Finite Element Method, 171–94. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-3363-9_8.
Khursheed, Anjam. "High-Order Elements." In The Finite Element Method in Charged Particle Optics, 99–110. Boston, MA: Springer US, 1999. http://dx.doi.org/10.1007/978-1-4615-5201-7_5.
Duczek, S., C. Willberg, and U. Gabbert. "Higher Order Finite Element Methods." In Lamb-Wave Based Structural Health Monitoring in Polymer Composites, 117–59. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49715-0_6.
Lin, Qun. "High Performance Finite Element Methods." In Recent Progress in Computational and Applied PDES, 269–88. Boston, MA: Springer US, 2002. http://dx.doi.org/10.1007/978-1-4615-0113-8_20.
Schöberl, Joachim, and Christoph Lehrenfeld. "Domain Decomposition Preconditioning for High Order Hybrid Discontinuous Galerkin Methods on Tetrahedral Meshes." In Advanced Finite Element Methods and Applications, 27–56. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-30316-6_2.
St.-Cyr, Amik, and Stephen J. Thomas. "High-Order Finite Element Methods for Parallel Atmospheric Modeling." In Lecture Notes in Computer Science, 256–62. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11428831_32.
Sabonnadière, Jean-Claude, and Jean-Louis Coulomb. "General theory of second order isoparametric elements." In Finite Element Methods in CAD, 91–103. New York, NY: Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4684-8739-8_5.
Sabonnadière, Jean-Claude, and Jean-Louis Coulomb. "General theory of second order isoparametric elements." In Finite Element Methods in CAD, 91–103. Boston, MA: Springer US, 1987. http://dx.doi.org/10.1007/978-1-4615-9879-4_5.
Cuvelier, C., A. Segal, and A. A. van Steenhoven. "Second Order Elliptic PDEs." In Finite Element Methods and Navier-Stokes Equations, 352–75. Dordrecht: Springer Netherlands, 1986. http://dx.doi.org/10.1007/978-94-010-9333-0_11.
Kyriakoudi, Konstantina C., and Michail A. Xenos. "Finite Element Methods with Higher Order Polynomials." In Exploring Mathematical Analysis, Approximation Theory, and Optimization, 161–76. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-46487-4_10.
Conference papers on the topic "High-Order finite element methods":
D'Aquila, Luke, Brian Helenbrook, and Alireza Mazaheri. "High-Order Shock Fitting with Finite Element Methods." In AIAA AVIATION 2020 FORUM. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2020. http://dx.doi.org/10.2514/6.2020-3047.
Woopen, Michael, Aravind Balan, and Georg May. "A Unifying Computational Framework for Adaptive High-Order Finite Element Methods." In 22nd AIAA Computational Fluid Dynamics Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2015. http://dx.doi.org/10.2514/6.2015-2601.
Kollmannsberger, Stefan, Alexander Du¨ster, and Ernst Rank. "Force Transfer for High Order Finite Element Methods Using Intersected Meshes." In ASME 2007 Pressure Vessels and Piping Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/pvp2007-26539.
Shumlak, U., R. Lilly, S. Miller, N. Reddell, and E. Sousa. "High-order finite element method for plasma modeling." In 2013 IEEE 40th International Conference on Plasma Sciences (ICOPS). IEEE, 2013. http://dx.doi.org/10.1109/plasma.2013.6634927.
Shumlak, U., R. Lilly, S. Miller, N. Reddell, and E. Sousa. "High-order finite element method for plasma modeling." In 2013 IEEE Pulsed Power and Plasma Science Conference (PPPS 2013). IEEE, 2013. http://dx.doi.org/10.1109/ppc.2013.6627593.
Sheshadri, Abhishek, and Antony Jameson. "Shock detection and capturing methods for high order Discontinuous-Galerkin Finite Element Methods." In 32nd AIAA Applied Aerodynamics Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2014. http://dx.doi.org/10.2514/6.2014-2688.
Shumlak, U., J. B. Coughlin, D. W. Crews, I. A. M. Datta, A. Ho, A. R. Johansen, E. T. Meier, Y. Takagaki, and W. R. Thomas. "High-Order Finite Element Method for High-Fidelity Plasma Modeling." In 2020 IEEE International Conference on Plasma Science (ICOPS). IEEE, 2020. http://dx.doi.org/10.1109/icops37625.2020.9717941.
Troutman, Roy, and Nelson L. Max. "Radiosity algorithms using higher order finite element methods." In the 20th annual conference. New York, New York, USA: ACM Press, 1993. http://dx.doi.org/10.1145/166117.166144.
Wang, Li, W. Kyle Anderson, and Lafayette K. Taylor. "Multiscale Large Eddy Simulation of Turbulence Using High-Order Finite Element Methods." In 7th AIAA Theoretical Fluid Mechanics Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2014. http://dx.doi.org/10.2514/6.2014-3211.
Taggar, Karanvir, Emad Gad, and Derek McNamara. "High-order unconditionally stable time-domain finite element method." In 2018 18th International Symposium on Antenna Technology and Applied Electromagnetics (ANTEM). IEEE, 2018. http://dx.doi.org/10.1109/antem.2018.8572958.
Reports on the topic "High-Order finite element methods":
Kirby, Robert M., and Robert Haimes. Visualization of High-Order Finite Element Methods. Fort Belvoir, VA: Defense Technical Information Center, August 2008. http://dx.doi.org/10.21236/ada500484.
Kirby, Robert M., and Robert Haimes. Visualization of High-Order Finite Element Methods. Fort Belvoir, VA: Defense Technical Information Center, March 2013. http://dx.doi.org/10.21236/ada578239.
Gao, Kai. Generalized and High-Order Multiscale Finite-Element Methods for Seismic Wave Propagation. Office of Scientific and Technical Information (OSTI), November 2018. http://dx.doi.org/10.2172/1481964.
Adjerid, Slimane, Mohammed Aiffa, and Joseph E. Flaherty. High-Order Finite Element Methods for Singularly-Perturbed Elliptic and Parabolic Problems. Fort Belvoir, VA: Defense Technical Information Center, December 1993. http://dx.doi.org/10.21236/ada290410.
White, D., M. Stowell, J. Koning, R. Rieben, A. Fisher, N. Champagne, and N. Madsen. Higher-Order Mixed Finite Element Methods for Time Domain Electromagnetics. Office of Scientific and Technical Information (OSTI), February 2004. http://dx.doi.org/10.2172/15014733.
Dobrev, V. A., F. C. Grogan, T. V. Kolev, R. Rieben, and V. Z. Tomov. Level set methods for detonation shock dynamics using high-order finite elements. Office of Scientific and Technical Information (OSTI), May 2017. http://dx.doi.org/10.2172/1361591.
Rieben, Robert N. A Novel High Order Time Domain Vector Finite Element Method for the Simulation of Electromagnetic Devices. Office of Scientific and Technical Information (OSTI), January 2004. http://dx.doi.org/10.2172/15014486.
Graville. L51764 Hydrogen Cracking in the Heat-Affected Zone of High-Strength Steels-Year 2. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), March 1997. http://dx.doi.org/10.55274/r0010170.
Jiang, W., and Benjamin W. Spencer. Modeling 3D PCMI using the Extended Finite Element Method with higher order elements. Office of Scientific and Technical Information (OSTI), March 2017. http://dx.doi.org/10.2172/1409274.
Chauhan. L52134 Development of Methods For Assessing Corrosion Metal Loss Defects In Casing Strings. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), July 2003. http://dx.doi.org/10.55274/r0010892.