Gradient discretisation method: Difference between revisions

Revision as of 12:11, 15 November 2016

Revision as of 21:20, 15 November 2016

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{{Differential equations}}

In numerical mathematics, the '''gradient discretisation method (GDM)''' is a framework which contains classical and recent discretisation schemes for diffusion problems of different kinds: linear or non -linear, steady-state or time-dependent. The schemes may be conforming or non -conforming and may rely on very general polygonal or polyhedral meshes.

Some core properties are required to prove the convergence of a GDM. Owing to these core properties, it is possible to prove the convergence of a GDM for standard elliptic and parabolic problems, linear or non-linear. As a consequence, any scheme entering the GDM framework is then known to converge on these problems; this occurs in the case of the conforming Finite Elements, the Raviart—Thomas Mixed Finite Elements, or the <math>P^1</math> non-conforming Finite Elements, or in the case of more recent schemes, such as the Hybrid Mixed Mimetic or Nodal Mimetic methods, some Discrete Duality Finite Volume schemes, and some Multi-Point Flux Approximation schemes.