van der Zee, K.G., van Brummelen, E.H. and De Borst, R. (2010) Goal-oriented error estimation and adaptivity for free-boundary problems: the shape-linearization approach. SIAM Journal on Scientific Computing, 32(2), pp. 1093-1118. (doi: 10.1137/080741239)
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Publisher's URL: http://dx.doi.org/10.1137/080741239
Abstract
We develop duality-based a posteriori error estimates for functional outputs of solutions of free-boundary problems via shape-linearization principles. To derive an appropriate dual (linearized adjoint) problem, we linearize the domain dependence of the very weak form and goal functional of interest using techniques from shape calculus. We show for a Bernoulli-type free-boundary problem that the dual problem corresponds to a Poisson problem with a Robin-type boundary condition involving the curvature. Moreover, we derive a generalization of the dual problem for nonsmooth free boundaries which includes a natural extension of the curvature term. The effectivity of the dual-based error estimate and its usefulness in goal-oriented adaptive mesh refinement is demonstrated by numerical experiments.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | De Borst, Professor Rene |
| Authors: | van der Zee, K.G., van Brummelen, E.H., and De Borst, R. |
| College/School: | College of Science and Engineering > School of Engineering > Infrastructure and Environment |
| Journal Name: | SIAM Journal on Scientific Computing |
| Publisher: | Society for Industrial and Applied Mathematics |
| ISSN: | 1064-8275 |
| ISSN (Online): | 1095-7197 |
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