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Worst-case multi-objective error estimation and adaptivity.
- Source :
-
Computer Methods in Applied Mechanics & Engineering . Jan2017, Vol. 313, p723-743. 21p. - Publication Year :
- 2017
-
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 estimate in adaptive refinement procedures. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00457825
- Volume :
- 313
- Database :
- Academic Search Index
- Journal :
- Computer Methods in Applied Mechanics & Engineering
- Publication Type :
- Academic Journal
- Accession number :
- 119927832
- Full Text :
- https://doi.org/10.1016/j.cma.2016.10.007