On 3D DDFV discretization of gradient and divergence operators. II. Discrete functional analysis tools and applications to degenerate parabolic problems.
Langue
en
Article de revue
Ce document a été publié dans
Computational Methods in Applied Mathematics. 2013-06, vol. 13, n° 4, p. pp. 369–410
De Gruyter
Résumé en anglais
We present a detailed survey of discrete functional analysis tools (consistency results, Poincaré and Sobolev embedding inequalities, discrete $W^{1,p}$ compactness, discrete compactness in space and in time) for the ...Lire la suite >
We present a detailed survey of discrete functional analysis tools (consistency results, Poincaré and Sobolev embedding inequalities, discrete $W^{1,p}$ compactness, discrete compactness in space and in time) for the so-called Discrete Duality (DDFV) Finite Volume schemes in three space dimensions. We concentrate mainly on the 3D CeVe-DDFV scheme presented in [3]. Some of our results are new, such as a general time-compactness result based upon the idea of Kruzhkov [65]; others generalize the ideas known for the 2D DDFV schemes or for traditional two-point finite volume schemes. We illustrate the use of these tools by studying convergence of discretizations of nonlinear elliptic-parabolic problems of Leray-Lions kind, and provide numerical results for this example.< Réduire
Mots clés en anglais
Finite volume approximation
Discrete duality
CeVe-DDFV
Convergence
Consistency
Discrete compactness
Discrete Sobolev embeddings
Degenerate parabolic problems
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