Convergence analysis of the high-order mimetic finite difference method

We prove second-order convergence of the conservative variable and its flux in the high-order MFD method. The convergence results are proved for unstructured polyhedral meshes and full tensor diffusion coefficients. For the case of non-constant coefficients, we also develop a new family of high-orde...

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Veröffentlicht in:	Numerische Mathematik 2009-09, Vol.113 (3), p.325-356
Hauptverfasser:	Beirão da Veiga, L., Lipnikov, K., Manzini, G.
Format:	Artikel
Sprache:	eng
Schlagworte:	Exact sciences and technology Mathematical and Computational Engineering Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Numerical Analysis Numerical analysis. Scientific computation Numerical and Computational Physics Sciences and techniques of general use Simulation Theoretical
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Zusammenfassung:	We prove second-order convergence of the conservative variable and its flux in the high-order MFD method. The convergence results are proved for unstructured polyhedral meshes and full tensor diffusion coefficients. For the case of non-constant coefficients, we also develop a new family of high-order MFD methods. Theoretical result are confirmed through numerical experiments.
ISSN:	0029-599X 0945-3245
DOI:	10.1007/s00211-009-0234-6