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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
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
Design and convergence analysis of numerical methods for stochastic evolution equations with Leray–Lions operator
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
A Gradient Discretisation Method for Anisotropic Reaction–Diffusion Models with Applications to the Dynamics of Brain Tumors
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
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
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
Numerical Analysis for the Pure Neumann Control Problem Using the Gradient Discretisation Method
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
Convergence analysis of some first order and second order time accurate gradient schemes for semilinear second order hyperbolic 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