Finite volume schemes for the biharmonic problem on general meshes (Q2840001)
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scientific article; zbMATH DE number 6188733
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Finite volume schemes for the biharmonic problem on general meshes |
scientific article; zbMATH DE number 6188733 |
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Finite volume schemes for the biharmonic problem on general meshes (English)
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17 July 2013
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biharmonic problem
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finite volume scheme
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convergence
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error estimate
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numerical tests
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The authors derive new finite volume schemes for the biharmonic equation with Dirichlet boundary conditions. The first part is concerning the convergence analysis when the mesh is satisfying an orthogonality condition. The convergence is shown under low regularity assumption on the exact solution and an error error estimate is proved when the exact solution is smooth. Similar results are also obtained when the mesh is general as in the paper by \textit{R. Eymard} et al. [IMA J. Numer. Anal. 30, No. 4, 1009--1043 (2010; Zbl 1202.65144)]. Numerical tests are presented to support the theoretical results.
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