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Gradient discretization of a 3D-2D-1D mixed-dimensional diffusive model with resolved interface, application to the drying of a fractured porous medium
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
Convergence analysis for a nonlinear system of parabolic variational inequalities
A Hybrid High-Order Method for Quasilinear Elliptic Problems of Nonmonotone Type
Thirupathi Gudi, Gouranga Mallik and Tamal Pramanick SIAM Journal on Numerical Analysis 60(4) 2318 (2022) https://doi.org/10.1137/21M1412050
A Virtual Element Method for the Wave Equation on Curved Edges in Two Dimensions
Franco Dassi, Alessio Fumagalli, Ilario Mazzieri, Anna Scotti and Giuseppe Vacca Journal of Scientific Computing 90(1) (2022) https://doi.org/10.1007/s10915-021-01683-w
Design and convergence analysis of numerical methods for stochastic evolution equations with Leray–Lions operator
Optimized Schwarz methods with general Ventcell transmission conditions for fully anisotropic diffusion with discrete duality finite volume discretizations
Martin J. Gander, Laurence Halpern, Florence Hubert and Stella Krell Moroccan Journal of Pure and Applied Analysis 7(2) 182 (2021) https://doi.org/10.2478/mjpaa-2021-0014
Polyhedral Methods in Geosciences
Paola F. Antonietti, Chiara Facciolà, Paul Houston, et al. SEMA SIMAI Springer Series, Polyhedral Methods in Geosciences 27 159 (2021) https://doi.org/10.1007/978-3-030-69363-3_5
Convergence of a positive nonlinear DDFV scheme for degenerate parabolic equations
Sharp algebraic and total a posteriori error bounds for h and p finite elements via a multilevel approach. Recovering mass balance in any situation
Jan Papež, Ulrich Rüde, Martin Vohralík and Barbara Wohlmuth Computer Methods in Applied Mechanics and Engineering 371 113243 (2020) https://doi.org/10.1016/j.cma.2020.113243
A robust and scalable multi-level domain decomposition preconditioner for multi-core architecture with large number of cores
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
Robust Numerical Methods for Nonlocal (and Local) Equations of Porous Medium Type. Part II: Schemes and Experiments
Félix del Teso, Jørgen Endal and Espen R. Jakobsen SIAM Journal on Numerical Analysis 56(6) 3611 (2018) https://doi.org/10.1137/18M1180748
Lowest-Order Weak Galerkin Finite Element Method for Darcy Flow on Convex Polygonal Meshes
Convergence Analysis of the mimetic Finite Difference Method for Elliptic Problems with Staggered Discretizations of Diffusion Coefficients
G. Manzini, K. Lipnikov, J. D. Moulton and M. Shashkov SIAM Journal on Numerical Analysis 55(6) 2956 (2017) https://doi.org/10.1137/16M1108479
Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects
J. Droniou and R. Eymard Springer Proceedings in Mathematics & Statistics, Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects 199 311 (2017) https://doi.org/10.1007/978-3-319-57397-7_24
The Gradient Discretization Method for Optimal Control Problems, with Superconvergence for Nonconforming Finite Elements and Mixed-Hybrid Mimetic Finite Differences
Jérome Droniou, Neela Nataraj and Devika Shylaja SIAM Journal on Control and Optimization 55(6) 3640 (2017) https://doi.org/10.1137/17M1117768
An analysis for the convergence order of gradient schemes for semilinear parabolic equations
Mimetic finite difference approximation of flows in fractured porous media
Paola F. Antonietti, Luca Formaggia, Anna Scotti, Marco Verani and Nicola Verzott ESAIM: Mathematical Modelling and Numerical Analysis 50(3) 809 (2016) https://doi.org/10.1051/m2an/2015087
Gradient schemes for the Signorini and the obstacle problems, and application to hybrid mimetic mixed methods