The Gradient Discretisation Method by Jérôme Droniou & Robert Eymard & Thierry Gallouët & Cindy Guichard & Raphaèle Herbin

Author:Jérôme Droniou & Robert Eymard & Thierry Gallouët & Cindy Guichard & Raphaèle Herbin
Language: eng
Format: epub
ISBN: 9783319790428
Publisher: Springer International Publishing

is a linear mapping.

The regularity factor is defined by (7.34).

Proposition 7.53

(GD-consistency of LLE GDs for non-homogeneous Dirichlet BCs) Let be a sequence of LLE GDs for non-homogeneous Dirichlet boundary conditions, in the sense of Definition 7.52. Denote by the mesh associated to . Assume that is bounded, that as , that (2.​96) holds, and that

(7.65)

Then is GD-consistent in the sense of Definition 2.​51.

Here and in the following, to simplify notations we make the convention that if .

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