A Local Mesh Modification Strategy for Interface Problems with Application to Shape and Topology Optimization
Numerical Analysis
2026-04-02 v1 Numerical Analysis
Abstract
We present and analyze a new finite element method for solving interface problems on a triangular grid. The method locally modifies a given triangulation such that the interfaces are accurately resolved and the maximal angle condition holds. Therefore, optimal order of convergence can be shown. Moreover, an appropriate scaling of the basis functions yields an optimal condition number of the stiffness matrix. The method is applied to an optimal design problem for an electric motor where the interface between different materials is evolving in the course of the optimization procedure.
Cite
@article{arxiv.1609.06236,
title = {A Local Mesh Modification Strategy for Interface Problems with Application to Shape and Topology Optimization},
author = {Peter Gangl and Ulrich Langer},
journal= {arXiv preprint arXiv:1609.06236},
year = {2026}
}
Comments
8 pages, 2 Figures, submitted to proceedings of SCEE (Scientific Computing in Electrical Engineering) 2016 in Strobl, Austria