The use of singular functions in the \(h\)--\(p\) version of the finite element method for a Dirichlet problem with degeneration of the input data (Q2773645)
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scientific article; zbMATH DE number 1710268
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The use of singular functions in the \(h\)--\(p\) version of the finite element method for a Dirichlet problem with degeneration of the input data |
scientific article; zbMATH DE number 1710268 |
Statements
24 February 2002
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singularity of the solution
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Dirichlet problem
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error bound
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second-order nonselfadjoint elliptic equation
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degeneration of input data
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\(h\)-\(p\) version of the finite element method
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convergence
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Sobolev space
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The use of singular functions in the \(h\)--\(p\) version of the finite element method for a Dirichlet problem with degeneration of the input data (English)
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The article is devoted to a Dirichlet problem for a second-order nonselfadjoint elliptic equation with a strong singularity of the solution caused by a coordinated degeneration of input data at boundary points of a two-dimensional domain. The \(h\)-\(p\) version of the finite element method is used to approximate this problem. The authors introduce a finite element space with a singular basis that depends on the space to which the solution to the problem belongs. It is proven that the convergence rate in the norm of a weighted Sobolev space is exponential.
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