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Asymptotic a posteriori finite element bounds for the outputs of noncoercive problems: the Helmholtz and Burgers equations

โœ Scribed by Jaume Peraire; Anthony T. Patera

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
560 KB
Volume
171
Category
Article
ISSN
0045-7825

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โœฆ Synopsis

We describe an a posteriori finite element procedure for the efficient computation of lower and upper estimators for linear-functional outputs of noncoercive linear and semilinear elliptic second-order partial differential equations. Under a relatively weak hypothesis related 10 the relat ive magn itude of the L' and H I errors of the reconstructed solut ion. these lower and upper est imators converge to the true output from below and above. respectively. and thus constitute asymptotic bounds. In numerical experiments we find that our hypothesis is satisfied once the finite element triangulation even roughly resolves the structure <Ifthe exact solution. and thus, in practice. the bounds prove quite reliable . Numerical resuhs are present ed for the one-dimensional Helmholtz equat ion and for the Burgers equation.

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