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arXiv · 1604.04541

Worst-case multi-objective error estimation and adaptivity

E. H. van Brummelen·S. Zhuk·G. J. van Zwieten
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Abstract

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 in adaptive refinement procedures.

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E. H. van Brummelen, S. Zhuk, G. J. van Zwieten. 2016-04-15. Worst-case multi-objective error estimation and adaptivity. https://doi.org/10.1016/j.cma.2016.10.007

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