Optimal Convergence Rates for Goal-Oriented FEM with Quadratic Goal Functional-Reference-Cited by-同舟云学术

Optimal Convergence Rates for Goal-Oriented FEM with Quadratic Goal Functional

Published:2020-10-21 Issue:2 Volume:21 Page:267-288
ISSN:1609-4840
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Becker Roland¹,Innerberger Michael²,Praetorius Dirk²

Affiliation:

1. Université de Pau et des Pays de l’Adour , IPRA-LMAP, Avenue de l’Université BP 1155, 64013 Pau Cedex , France

2. TU Wien , Institute of Analysis and Scientific Computing , Wiedner Hauptstr. 8–10/E101/4, 1040 Vienna , Austria

Abstract

Abstract We consider a linear elliptic PDE and a quadratic goal functional. The goal-oriented adaptive FEM algorithm (GOAFEM) solves the primal as well as a dual problem, where the goal functional is always linearized around the discrete primal solution at hand. We show that the marking strategy proposed in [M. Feischl, D. Praetorius and K. G. van der Zee, An abstract analysis of optimal goal-oriented adaptivity, SIAM J. Numer. Anal. 54 (2016), 3, 1423–1448] for a linear goal functional is also optimal for quadratic goal functionals, i.e., GOAFEM leads to linear convergence with optimal convergence rates.

Funder

Austrian Science Fund

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

Reference26 articles.

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