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Approximate Riesz representatives of shape gradients

IFIP Advances in Information and Communication Technology (2016) 494 399-409
DOI: 10.1007/978-3-319-55795-3_38
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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 H1-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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Paganini, A., & Hiptmair, R. (2016). Approximate Riesz representatives of shape gradients. In IFIP Advances in Information and Communication Technology (Vol. 494, pp. 399–409). Springer New York LLC. https://doi.org/10.1007/978-3-319-55795-3_38

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