The Gradient Discretisation Method - Droniou Jérôme

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Résumé :
This monograph presents the Gradient Discretisation Method (GDM), which is a unified convergence analysis framework for numerical methods for elliptic and parabolic partial differential equations. The results obtained by the GDM cover both stationary and transient models . error estimates are provided for linear (and some non-linear) equations, and convergence is established for a wide range of fully nonlinear models (e.g. Leray-Lions equations and degenerate parabolic equations such as the Stefan or Richards models). The GDM applies to a diverse range of methods, both classical (conforming, non-conforming, mixed finite elements, discontinuous Galerkin) and modern (mimetic finite differences, hybrid and mixed finite volume, MPFA-O finite volume), some of which can be built on very general meshes.

Biographie:

J?r?me Droniou is Associate Professor at Monash University, Australia. His research focuses on elliptic and parabolic PDEs. He has published many papers on theoretical and numerical analysis of models with singularities or degeneracies, including convergence analysis of schemes without regularity assumptions on the data or solutions.

Robert Eymard is professor of mathematics at Universit? Paris-Est Marne-la-Vall?e. His research concerns the design and analysis of numerical methods, mainly applied to fluid flows in porous media and incompressible Navier-Stokes equations.

Thierry Gallouet is professor at the University of Aix-Marseille. His research focuses on the analysis of partial differential equations and the approximation of their solutions by numerical schemes.