The optimal rate of convergence of the \(p\)-version of the boundary element method in two dimensions (Q704804)
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scientific article; zbMATH DE number 2130176
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The optimal rate of convergence of the \(p\)-version of the boundary element method in two dimensions |
scientific article; zbMATH DE number 2130176 |
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The optimal rate of convergence of the \(p\)-version of the boundary element method in two dimensions (English)
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19 January 2005
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The authors formulate two theorems concerning the optimal convergence of the \(p\)-version of the boundary element solution to the boundary integral equations of the first kind corresponding to Dirichlet and Neumann problems for Laplace's equation. In order to prove these results they introduce some elements of the approximation theory such as the approximability of functions in the Jacobi-weighted Besov and Sobolev spaces.
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Laplace's equation
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Dirichlet and Neumann problems
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boundary element method
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p-version
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hypersingular operators
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weakly singular integral operators
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2D polygonal domains
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energy norms
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convergence
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boundary integral equations
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Besov space
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Sobolev space
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