Convergence of the difference scheme of the finite element method for the Poisson equation in the metric \(L_ p\) (Q760195)
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scientific article; zbMATH DE number 3883554
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Convergence of the difference scheme of the finite element method for the Poisson equation in the metric \(L_ p\) |
scientific article; zbMATH DE number 3883554 |
Statements
Convergence of the difference scheme of the finite element method for the Poisson equation in the metric \(L_ p\) (English)
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1984
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The convergence analysis is performed by means of finite-difference techniques: An a priori bound (in discrete \(L_ p\)-norm) of the solution error by the residuum of the difference equation is found. As a consequence, error estimates of the types O(h) and \(O(h^ 2)\), respectively, are derived assuming regularities \(W^{1,p}(p>2)\) and \(W^{2,p}(p>1)\) of the exact solution.
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Dirichlet problem
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Poisson equation
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finite element method
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difference boundary value problem
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finite-difference techniques
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