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Convergence of nonlinear finite volume schemes for two-phase porous media flow on general meshes
Léo Agélas, Martin Schneider, Guillaume Enchéry and Bernd Flemisch IMA Journal of Numerical Analysis 42(1) 515 (2022) https://doi.org/10.1093/imanum/draa064
A linearity-preserving technique for finite volume schemes of anisotropic diffusion problems on polygonal meshes
Comparison of finite-volume schemes for diffusion problems
Martin Schneider, Dennis Gläser, Bernd Flemisch, et al. Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles 73 82 (2018) https://doi.org/10.2516/ogst/2018064
ArcFVDSL, a DSEL Combined to HARTS, a Runtime System Layer to Implement Efficient Numerical Methods to Solve Diffusive Problems on New Heterogeneous Hardware Architecture
Jean-Marc Gratien and S. de Chaisemartin Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles 72(2) 12 (2017) https://doi.org/10.2516/ogst/2017007
A virtual volume method for heterogeneous and anisotropic diffusion-reaction problems on general meshes
An a posteriori-based, fully adaptive algorithm with adaptive stopping criteria and mesh refinement for thermal multiphase compositional flows in porous media
A Review of Recent Advances in Discretization Methods,a PosterioriError Analysis, and Adaptive Algorithms for Numerical Modeling in Geosciences
Daniele A. Di Pietro and Martin Vohralík Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles 69(4) 701 (2014) https://doi.org/10.2516/ogst/2013158
Finite volume schemes for diffusion equations: Introduction to and review of modern methods
Numerical comparison of robustness of some reduction methods in rough grids
Jiangyong Hou, Shuyu Sun and Zhangxin Chen Numerical Methods for Partial Differential Equations 30(5) 1484 (2014) https://doi.org/10.1002/num.21873
MIXED FINITE ELEMENT METHODS: IMPLEMENTATION WITH ONE UNKNOWN PER ELEMENT, LOCAL FLUX EXPRESSIONS, POSITIVITY, POLYGONAL MESHES, AND RELATIONS TO OTHER METHODS
Modelling and Simulation in Fluid Dynamics in Porous Media
J.-M. Gratien Springer Proceedings in Mathematics & Statistics, Modelling and Simulation in Fluid Dynamics in Porous Media 28 157 (2013) https://doi.org/10.1007/978-1-4614-5055-9_10
A domain-specific embedded language in C++ for lowest-order discretizations of diffusive problems on general meshes
Finite Volumes for Complex Applications VI Problems & Perspectives
Daniele A. Di Pietro and Jean-Marc Gratien Springer Proceedings in Mathematics, Finite Volumes for Complex Applications VI Problems & Perspectives 4 803 (2011) https://doi.org/10.1007/978-3-642-20671-9_84
Correction non linéaire et principe du maximum pour la discrétisation d'opérateurs de diffusion avec des schémas volumes finis centrés sur les mailles