Leugering G, Friederich J, Steinmann P (2014)
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2014
Publisher: Systems Research Institute
Book Volume: 43
Pages Range: 279-306
Journal Issue: 2
URI: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85018838294&origin=inward
We propose a novel approach to adaptive refinement in FEM based on local sensitivities for node insertion. To this end, we consider refinement as a continuous graph operation, for instance by splitting nodes along edges. Thereby, we introduce the concept of the topological mesh derivative for a given objective function. For its calculation, we rely on the first-order asymptotic expansion of the Galerkin solution of a symmetric linear second-order elliptic PDE. In this work, we apply this concept to the total potential energy, which is related to the approximation error in the energy norm. In fact, our approach yields local sensitivities for minimization of the energy error by refinement. Moreover, we prove that our indicator is equivalent to the classical explicit a posteriori error estimator in a certain sense. Numerical results suggest that our method leads to efficient and competitive adaptive refinement.
APA:
Leugering, G., Friederich, J., & Steinmann, P. (2014). Adaptive finite elements based on sensitivities for topological mesh changes. Control and Cybernetics, 43(2), 279-306.
MLA:
Leugering, Günter, Jan Friederich, and Paul Steinmann. "Adaptive finite elements based on sensitivities for topological mesh changes." Control and Cybernetics 43.2 (2014): 279-306.
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