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Convergence analysis of the high-order mimetic finite difference method |
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| Authors: | L. Beirão da Veiga K. Lipnikov G. Manzini |
| Affiliation: | (1) Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, via Saldini 50, 20133 Milano, Italy;(2) Los Alamos National Laboratory, Theoretical Division, MS B284, Los Alamos, NM 87545, USA;(3) Istituto di Matematica Applicata e Tecnologie Informatiche (IMATI), CNR, via Ferrata 1, 27100 Pavia, Italy |
| 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. |
| Keywords: | Mathematics Subject Classification (2000) 65N12 |
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