Solving obstacle problems with guaranteed accuracy. (Q1416447)
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scientific article; zbMATH DE number 2017235
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Solving obstacle problems with guaranteed accuracy. |
scientific article; zbMATH DE number 2017235 |
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Solving obstacle problems with guaranteed accuracy. (English)
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14 December 2003
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The author sets out to find numerically guaranteed inclusion bounds for a nonlinear obstacle problem. This proceeds by reformulating the variational inequality of the obstacle problem into a fixed point of a compact operator. As the author wants to use Schauder's fixed point theorem, he constructs an algorithm to find a set which is mapped into itself by the operator in a finite element discretisation. The result of this algorithm is an approximate solution to the obstacle problem where the existence of a solution has been verified numerically. Interval arithmetic is used to carry out the computations numerically. The paper closes with two numerical examples.
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Numerical verification
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Error estimates
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Finite element method
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nonlinear obstacle problem
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variational inequality
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algorithm
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interval arithmetic
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numerical examples
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Schauder's fixed point theorem
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