The Gradient Discretisation Method

Beschreibung

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 non-linear 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.
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 non-linear 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.
Includes a complete convergence analysis of schemes for linear and non-linear PDEs, covering all standard boundary conditions for elliptic and parabolic models Presents a unified analysis of many classical, and less classical, numerical methods, including an analysis of degenerate models Provides very generic compactness results for stationary and time-dependent problems

Autor*in

Jérôme Droniou

Themen in »The Gradient Discretisation Method«

Gradient Discretisation Method Gradient schemes Elliptic partial differential equations Parabolic partial differential equations Unified convergence analysis Discrete Aubin-Simon compactness theorems Convergence by compactness Error estimates partial differential equations

Stimmen zu »The Gradient Discretisation Method«

Details

Link teilen