Instance-Optimal Goal-Oriented Adaptivity-Reference-Cited by-同舟云学术

Instance-Optimal Goal-Oriented Adaptivity

Published:2020-02-18 Issue:1 Volume:21 Page:109-126
ISSN:1609-4840
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Innerberger Michael¹,Praetorius Dirk¹

Affiliation:

1. Institute for Analysis and Scientific Computing , TU Wien , Wiedner Hauptstr. 8–10/E101/4, 1040 Wien , Austria

Abstract

Abstract We consider an adaptive finite element method with arbitrary but fixed polynomial degree p ≥ 1

{p\geq 1}

, where adaptivity is driven by an edge-based residual error estimator. Based on the modified maximum criterion from [L. Diening, C. Kreuzer and R. Stevenson, Instance optimality of the adaptive maximum strategy, Found. Comput. Math. 16 2016, 1, 33–68], we propose a goal-oriented adaptive algorithm and prove that it is instance optimal. More precisely, the goal error is bounded by the product of the total errors (being the sum of energy error plus data oscillations) of the primal and the dual problem, and the proposed algorithm is instance optimal with respect to this upper bound. Numerical experiments underline our theoretical findings.

Funder

Austrian Science Fund

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

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