Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes (Q2707088)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes |
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Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes (English)
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19 November 2001
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mesh refinement
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convection-diffusion equation
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finite volume method
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convergence
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error estimate
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The numerical solution of the linear two-dimensional convection-diffusion equation, with mixed Dirichlet and Neumann boundary conditions, is considered. For the approximation the finite volume method on Cartesian meshes refined using an automatic technique is proposed. This technique leads to meshes with hanging nodes. An analysis through a discrete variational approach in a discrete \(H^1\) finite volume space is used. The convergence of this scheme in a discrete \(H^1\) norm, with an error estimate of order \(O(h)\), where \(h\) is the size of the mesh is proved.
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