Constants in Clément-interpolation error and residual based a posteriori error estimates in finite element methods (Q2708277)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Constants in Clément-interpolation error and residual based a posteriori error estimates in finite element methods |
scientific article |
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3 December 2001
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a posteriori error estimate
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adaptive algorithm
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reliability
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Poincaré's inequality
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Friedrichs' inequality
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finite element methods
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Laplace equations
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numerical experiments
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0.87301767
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0.8723545
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0.86701167
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0.86339426
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0.86026216
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0.85970426
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Constants in Clément-interpolation error and residual based a posteriori error estimates in finite element methods (English)
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Residual based adaptive finite element methods applied to Laplace equations involve constants:NEWLINENEWLINENEWLINE-- in front of a weighted volume term;NEWLINENEWLINENEWLINE-- in front of weighted stress jumps across inner-element boundaries. NEWLINENEWLINENEWLINEThe aim of this paper is to establish explicit formulae for these constants by using the shape of the elements only. This leads to a straightforward hard-analysis, the results of which are compared with some numerical experiments reported in the final section of the work.NEWLINENEWLINENEWLINEIn some way, this paper puts the final piece to a class of a fully reliable a posteriori finite element error analysis.
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