Backward Euler method for abstract time-dependent parabolic equations with variable domains (Q1806012)
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scientific article; zbMATH DE number 1356179
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Backward Euler method for abstract time-dependent parabolic equations with variable domains |
scientific article; zbMATH DE number 1356179 |
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Backward Euler method for abstract time-dependent parabolic equations with variable domains (English)
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1 November 1999
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For linear parabolic problems with time-dependent operator, the temporal discretization by means of the implicit Euler method is studied in an abstract Banach space setting. This covers also problems with time-dependent non-homogeneous right-hand side and boundary conditions. The author proves new general results in the situation of operators with time-dependent domain of definition. Error estimates are obtained for sufficiently smooth exact solutions and operators being Hölder continuous. Finally, the author shows how classical problems meet the new framework.
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time discretization
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backward Euler method
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error estimates
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linear parabolic problems
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implicit Euler method
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Banach space
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