Global convergence of $W^{1,\infty}$-steepest descent for PDE constrained shape optimisation with semilinear elliptic equations in function space

Klaus Deckelnick; Philip J. Herbert; Michael Hinze

doi:10.48550/arxiv.2603.02812

Global convergence of $W^{1,\infty}$-steepest descent for PDE constrained shape optimisation with semilinear elliptic equations in function space

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Klaus Deckelnick, Philip J. Herbert, Michael Hinze

DOI: 10.48550/arxiv.2603.02812

Cited by: 0

Abstract

We prove global convergence in function space for the steepest descent method in shape optimisation with semilinear elliptic partial differential equations. Steepest descent is realized in the Lipschitz topology. In addition, we prove a conditional convergence result for the resulting shapes in two space dimensions.

Fields of Study & Subjects

Advanced Numerical Methods in Computational Mathematics Topology Optimization in Engineering Geometric Analysis and Curvature Flows

Publication details

Journal / source: arXiv (Cornell University)
Publication date: 3 March 2026
Language: EN
Document type: Preprint