Speaker
Dennis Trautwein, University of Regensburg and Ganghui Zhang, University of Oxford
Abstract
We present a parametric finite element formulation for structure-preserving numerical methods. Our approach introduces two scalar Lagrange multipliers and evolution equations for surface energy and volume, ensuring that the resulting schemes maintain the underlying geometric and physical structures. To illustrate the method, we discuss two examples: surface diffusion and two-phase Stokes flow. By combining piecewise linear parametric finite elements in space with structure-preserving second-order time discretizations, we obtain fully discrete schemes of high temporal accuracy. We also address efficient strategies for solving the arising nonlinear systems and their linear subproblems. Numerical experiments confirm that the proposed methods achieve the expected accuracy while preserving surface energy and volume.