The Gradient Discretisation Method - Cindy Guichard,Robert Eymard,Raphaèle Herbin,Thierry Gallouët,Jérôme Droniou
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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-lin ... Full description
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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.
More Information
| Author | Cindy Guichard, Robert Eymard, Raphaèle Herbin, Thierry Gallouët, Jérôme Droniou |
|---|---|
| Publisher | Springer Nature Switzerland |
| Series | Mathématiques et Applications |
| Release year | 2018 |
| Cover type | Softcover |
| EAN | 9783319790411 |