Approximate Riesz Representatives of Shape Gradients

Abstract : We study finite element approximations of Riesz representatives of shape gradients. First, we provide a general perspective on its error analysis. Then, we focus on shape functionals constrained by elliptic boundary value problems and $$H^1$$-representatives of shape gradients. We prove linear convergence in the energy norm for linear Lagrangian finite element approximations. This theoretical result is confirmed by several numerical experiments.
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Alberto Paganini, Ralf Hiptmair. Approximate Riesz Representatives of Shape Gradients. 27th IFIP Conference on System Modeling and Optimization (CSMO), Jun 2015, Sophia Antipolis, France. pp.399-409, ⟨10.1007/978-3-319-55795-3_38⟩. ⟨hal-01626913⟩

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