EAN: 9783319790411

THE GRADIENT DISCRETISATION METHOD - JÉRÔME DRO...

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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