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Data-driven Whitney forms for structure-preserving control volume analysis
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Two Finite Element Approaches for the Porous Medium Equation That Are Positivity Preserving and Energy Stable
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Numerical Methods for Mixed Finite Element Problems
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Well-Posedness and Discretization for a Class of Models for Mixed-Dimensional Problems with High-Dimensional Gap
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A Finite-Element Framework for a Mimetic Finite-Difference Discretization of Maxwell's Equations
James H. Adler, Casey Cavanaugh, Xiaozhe Hu and Ludmil T. Zikatanov SIAM Journal on Scientific Computing 43(4) A2638 (2021) https://doi.org/10.1137/20M1382568
Multigrid solvers for multipoint flux approximations of the Darcy problem on rough quadrilateral grids
H1‐superconvergence of finite difference method based on Q1‐element on quasi‐uniform mesh for the 3D Poisson equation
Xinlong Feng, Ruijian He and Zhangxin Chen Numerical Methods for Partial Differential Equations 36(1) 29 (2020) https://doi.org/10.1002/num.22386
Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples
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An enriched finite volume formulation for the simulation of ductile material failure under shock loading
Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples
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Numerical Methods and Applications
Francisco J. Gaspar, Carmen Rodrigo, Xiaozhe Hu, et al. Lecture Notes in Computer Science, Numerical Methods and Applications 11189 3 (2019) https://doi.org/10.1007/978-3-030-10692-8_1
Multipoint flux mixed finite element methods for slightly compressible flow in porous media
Higher order multipoint flux mixed finite element methods on quadrilaterals and hexahedra
Ilona Ambartsumyan, Eldar Khattatov, Jeonghun J. Lee and Ivan Yotov Mathematical Models and Methods in Applied Sciences 29(06) 1037 (2019) https://doi.org/10.1142/S0218202519500167
Raviart–Thomas finite elements of Petrov–Galerkin type
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Encyclopedia of Computational Mechanics Second Edition
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François Dubois, Isabelle Greff and Charles Pierre Springer Proceedings in Mathematics & Statistics, Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects 199 341 (2017) https://doi.org/10.1007/978-3-319-57397-7_27
𝐻¹-Superconvergence of a difference finite element method based on the 𝑃₁-𝑃₁-conforming element on non-uniform meshes for the 3D Poisson equation
A nonconforming finite element method for the Biot’s consolidation model in poroelasticity
Xiaozhe Hu, Carmen Rodrigo, Francisco J. Gaspar and Ludmil T. Zikatanov Journal of Computational and Applied Mathematics 310 143 (2017) https://doi.org/10.1016/j.cam.2016.06.003
MIXED FINITE ELEMENT METHODS: IMPLEMENTATION WITH ONE UNKNOWN PER ELEMENT, LOCAL FLUX EXPRESSIONS, POSITIVITY, POLYGONAL MESHES, AND RELATIONS TO OTHER METHODS
Daniele Boffi, Franco Brezzi and Michel Fortin Springer Series in Computational Mathematics, Mixed Finite Element Methods and Applications 44 401 (2013) https://doi.org/10.1007/978-3-642-36519-5_7
Time Discretization Schemes for Poincaré Waves in Finite-Element Shallow-Water Models
Daniel Y. Le Roux, Michel Dieme and Abdou Sene SIAM Journal on Scientific Computing 33(5) 2217 (2011) https://doi.org/10.1137/090779413
A Multipoint Flux Mixed Finite Element Method on Hexahedra
A conservative and monotone mixed-hybridized finite element approximation of transport problems in heterogeneous domains
Marco Brera, Joseph W. Jerome, Yoichiro Mori and Riccardo Sacco Computer Methods in Applied Mechanics and Engineering 199(41-44) 2709 (2010) https://doi.org/10.1016/j.cma.2010.05.016
Error estimates for the finite volume discretization for the porous medium equation
I.S. Pop, M. Sepúlveda, F.A. Radu and O.P. Vera Villagrán Journal of Computational and Applied Mathematics 234(7) 2135 (2010) https://doi.org/10.1016/j.cam.2009.08.071
A finite volume method on general surfaces and its error estimates
Impact of mass lumping on gravity and Rossby waves in 2D finite‐element shallow‐water models
D. Y. Le Roux, E. Hanert, V. Rostand and B. Pouliot International Journal for Numerical Methods in Fluids 59(7) 767 (2009) https://doi.org/10.1002/fld.1837
A posteriori error analysis of a cell-centered finite volume method for semilinear elliptic problems
Don Estep, Michael Pernice, Du Pham, Simon Tavener and Haiying Wang Journal of Computational and Applied Mathematics 233(2) 459 (2009) https://doi.org/10.1016/j.cam.2009.07.046
Mary F. Wheeler and Ivan Yotov The IMA Volumes in Mathematics and its Applications, Compatible Spatial Discretizations 142 189 (2006) https://doi.org/10.1007/0-387-38034-5_10
Equivalence between lowest-order mixed finite element and multi-point finite volume methods on simplicial meshes
Flux-upwind stabilization of the discontinuous Petrov–Galerkin formulation with Lagrange multipliers for advection-diffusion problems
Paola Causin, Riccardo Sacco and Carlo L. Bottasso ESAIM: Mathematical Modelling and Numerical Analysis 39(6) 1087 (2005) https://doi.org/10.1051/m2an:2005050
A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids
The maximum principle violations of the mixed-hybrid finite-element method applied to diffusion equations
H. Hoteit, R. Mosé, B. Philippe, Ph. Ackerer and J. Erhel International Journal for Numerical Methods in Engineering 55(12) 1373 (2002) https://doi.org/10.1002/nme.531
On Some Mixed Finite Element Methods with Numerical Integration
Transient Numerical Simulation of Combustion in Inert Porous Media
P. Knabner, M. J. De Neef and G. Summ ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 79(S1) 45 (1999) https://doi.org/10.1002/zamm.19990791312