Vertex-centered finite volume schemes of any order over quadrilateral meshes for elliptic boundary value problems (Q888524)
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scientific article; zbMATH DE number 6502662
| Language | Label | Description | Also known as |
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| English | Vertex-centered finite volume schemes of any order over quadrilateral meshes for elliptic boundary value problems |
scientific article; zbMATH DE number 6502662 |
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Vertex-centered finite volume schemes of any order over quadrilateral meshes for elliptic boundary value problems (English)
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30 October 2015
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The finite volume scheme over quadrilateral meshes is analyzed in the case of its application for the solution of an elliptic boundary value problem. The framework of the Petrov-Galerkin method is used. With the aid of a special mapping from the trial space to the test space, a unified proof for the inf-sup condition of any order finite volume schemes is provided, where the condition that the underlying mesh is a parallelogram mesh is employed. The optimal convergence rate of finite volume solutions is then obtained.
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finite volume method
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Petrov-Galerkin method
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inf-sup condition
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convergence
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quadrilateral meshes
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elliptic boundary value problem
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