Reliability and efficiency of DWR-type a posteriori error estimates with smart sensitivity weight recovering

2020/03/19 by Endtmayer, Bernhard, Langer, Ulrich, Wick, Thomas
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2003.08999

Abstract

We derive efficient and reliable goal-oriented error estimations, and devise adaptive mesh procedures for the finite element method that are based on the localization of a posteriori estimates. In our previous work [SIAM J. Sci. Comput., 42(1), A371--A394, 2020], we showed efficiency and reliability for error estimators based on enriched finite element spaces. However, the solution of problems on a enriched finite element space is expensive. In the literature, it is well known that one can use some higher-order interpolation to overcome this bottleneck. Using a saturation assumption, we extend the proofs of efficiency and reliability to such higher-order interpolations. The results can be used to create a new family of algorithms, where one of them is tested on three numerical examples (Poisson problem, p-Laplace equation, Navier-Stokes benschmark), and is compared to our previous algorithm.

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