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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
Analysis of the decoupled and positivity-preserving DDFV schemes for 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
A third Strang lemma and an Aubin–Nitsche trick for schemes in fully discrete formulation
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 two-step finite volume method to discretize heterogeneous and anisotropic pressure equation on general grids
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
A posteriori error estimates, stopping criteria, and adaptivity for multiphase compositional Darcy flows in porous media
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
MIXED FINITE ELEMENT METHODS: IMPLEMENTATION WITH ONE UNKNOWN PER ELEMENT, LOCAL FLUX EXPRESSIONS, POSITIVITY, POLYGONAL MESHES, AND RELATIONS TO OTHER METHODS
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
A compact cell-centered Galerkin method with subgrid stabilization