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The Gradient Discretisation Method, Paperback / softback Book

The Gradient Discretisation Method Paperback / softback

Part of the Mathematiques et Applications series

Paperback / softback

Description

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.

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