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.
Convergence analysis of the high-order mimetic finite difference method / L. Beirao da Veiga, K. Lipnikov, G. Manzini. - In: NUMERISCHE MATHEMATIK. - ISSN 0029-599X. - 113:3(2009), pp. 325-356. [10.1007/s00211-009-0234-6]
Convergence analysis of the high-order mimetic finite difference method
L. Beirao da VeigaPrimo
;
2009
Abstract
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.
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