An anisotropic error indicator based on Zienkiewicz-Zhu error estimator: Application to elliptic and parabolic problems

The anisotropic error indicator presented in [M. Picasso, Comm. Numer. Methods Engrg., 19 (2003), pp. 13--23.] in the frame of the Laplace equation is extended to elliptic and parabolic problems. Our error indicator is derived using the anisotropic interpolation estimates of [L. Formaggia and S. Per...

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Bibliographic Details
Published in:SIAM journal on scientific computing 2003, Vol.24 (4), p.1328-1355
Main Author: PICASSO, M
Format: Article
Language:English
Subjects:
Decomposition
Estimates
Exact sciences and technology
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Sciences and techniques of general use
Textbooks
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Summary:The anisotropic error indicator presented in [M. Picasso, Comm. Numer. Methods Engrg., 19 (2003), pp. 13--23.] in the frame of the Laplace equation is extended to elliptic and parabolic problems. Our error indicator is derived using the anisotropic interpolation estimates of [L. Formaggia and S. Perotto, Numer. Math., 89 (2001), pp. 641--667; L. Formaggia and S. Perotto, Numer. Math., (2002), DOI 10.1007/s002110200415], together with a Zienkiewicz--Zhu error estimator to approach the error gradient. A numerical study of the effectivity index is proposed for elliptic, diffusion-convection, and parabolic problems. An adaptive algorithm is implemented, aimed at controlling the relative estimated error.
ISSN:1064-8275
1095-7197
DOI:10.1137/S1064827501398578