Supraconvergent cell-centered scheme for two dimensional elliptic problems (Q960289)
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scientific article; zbMATH DE number 5382929
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Supraconvergent cell-centered scheme for two dimensional elliptic problems |
scientific article; zbMATH DE number 5382929 |
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Supraconvergent cell-centered scheme for two dimensional elliptic problems (English)
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16 December 2008
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The author considers a two-dimensional elliptic equation with variable coefficients subject to Dirichlet boundary value conditions in a domain, consisting of a union of rectangles. A cell-centered finite difference scheme on nonuniform meshes is studied. By means of appropriate negative norms, a supraconvergence and second-order error estimates in a discrete \(L^{2}(\Omega )\)-norm are proved if the exact solution of the problem is in the Sobolev space \(H^{4}(\Omega )\). A numerical example is given.
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finite difference scheme
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cell-centered scheme
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nonuniform mesh
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supraconvergence
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