Worst-case multi-objective error estimation and adaptivity

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• 作者：E.H. van Brummelen^a ; ^{e.h.v.brummelen@tue.nl} ; S. Zhuk^b ; G.J. van Zwieten^a
• 关键词：A-posterior error estimation ; Worst-case multi-objective error estimation ; Adaptive finite-element methods
• 刊名：Computer Methods in Applied Mechanics and Engineering
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：313
• 期：Complete
• 页码：723-743
• 全文大小：1790 K
• 卷排序：313

文摘

This paper introduces a new computational methodology for determining a-posteriori multi-objective error estimates for finite-element approximations, and for constructing corresponding (quasi-)optimal adaptive refinements of finite-element spaces. As opposed to the classical goal-oriented approaches, which consider only a single objective functional, the presented methodology applies to general closed convex subsets of the dual space and constructs a worst-case error estimate of the finite-element approximation error. This worst-case multi-objective error estimate conforms to a dual-weighted residual, in which the dual solution is associated with an approximate supporting functional of the objective set at the approximation error. We regard both standard approximation errors and data-incompatibility errors associated with incompatibility of boundary data with the trace of the finite-element space. Numerical experiments are presented to demonstrate the efficacy of applying the proposed worst-case multi-objective error estimate in adaptive refinement procedures.