New recovery based a posteriori error estimators


Advanced Numerical Methods for Scientific Computing
MOX 52
New recovery based a posteriori error estimators
Thursday 25th November 2004
Bottasso, Carlo L.; Maisano, Giorgio; Micheletti, Stefano; Perotto, Simona
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In this paper we formulate some new a posteriori recovery-based error estimators. The first one provides us with an improved approximation for the solution gradient. The other two furnish and estimate for the $L^2$-norm of the error on the solution itself. In more detail, the first estimator is a variant of the well-known Zienckiewicz-Zhu method and it turns out to be exact 1D for quadratic solution on non-uniform grids. The second one is based on a solution enrichment relying upon the Zienckiewicz-zhu recovered gradient. Finally the third estimator consists of a roughening of the solution followed by a Zienckiewicz-Zhu-like recovery applied to the solution itself. The three new proposed methods are compared in terms of their effectivity indices and solution accuracy on two and three dimensional problems
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Bottasso, C. L.; Maisano, G.; Micheletti, S.; Perotto, S., On some new recovery based a posteriori error estimators, Comput. Methods Appl. Mech. Engrg., 195 (2006), no. 37-40, 4794-4815