A discontinuous finite volume element method for second‐order elliptic problems |
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Authors: | Chunjia Bi Mingming Liu |
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Affiliation: | Department of Mathematics, Yantai University, Shandong 264005, China |
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Abstract: | In this article, we propose a new discontinuous finite volume element (DFVE) method for the second‐order elliptic problems. We treat the DFVE method as a perturbation of the interior penalty method and get a superapproximation estimate in a mesh dependent norm between the solution of the DFVE method and that of the interior penalty method. This reveals that the DFVE method is much closer to the interior penalty method than we have known. By using this superapproximation estimate, we can easily get the optimal order error estimates in the L2 ‐norm and in the maximum norms of the DFVE method.© 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 425–440, 2012 |
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Keywords: | discontinuous finite volume element method elliptic problems error estimates the interior penalty method |
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