Adaptive finite elements based on sensitivities fortopological mesh changes

• Autorzy: Friederich J. , Leugering G. , Steinmann P.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

adaptive mesh refinement; sensitivity-based refinement; topological sensitivity; asymptotic expansion

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2014
• Tom: Vol. 43, no. 2
• Strony: 279--306
• Opis fizyczny: Bibliogr. 32 poz., rys.

Twórcy

autor

Friederich J.

• Chair of Applied Mechanics, Friedrich-Alexander University Erlangen, Egerlandstr. 5, 91058 Erlangen, Germany

autor

Leugering G.

• Chair of Applied Mathematics 2, Friedrich-Alexander University Erlangen, Cauerstr. 11, 91058 Erlangen, Germany
• [e-mail]

autor

Steinmann P.

• Chair of Applied Mechanics, Friedrich-Alexander University Erlangen, Egerlandstr. 5, 91058 Erlangen, Germany

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