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Daily Overview |
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NEE2: Nonlinear Evolution Equations and Applications Location: F420 Session Chair: Bogdan-Vasile Matioc | |
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An MBO Scheme for Approximating Mean Curvature Flow with Obstacles Heidelberg University, Germany We propose a new method for approximating mean curvature flow with obstacles. The scheme is an adaptation of the celebrated thresholding method of Merriman, Bence, and Osher (MBO). Despite its computational efficiency, the proposed approach is unconditionally stable, monotone, and enforces the obstacle constraints exactly. The main focus of this talk is the convergence analysis of the scheme. We prove convergence to viscosity solutions of mean curvature flow with obstacles using a comparison-principle-based framework. In addition, we discuss suitable spatial discretizations and investigate their convergence behavior in practice. The proposed approach naturally extends to several important variants of the MBO scheme, including volume-preserving, anisotropic, and multiphase formulations. While these extensions appear promising from a computational perspective, their rigorous convergence analysis remains open. This raises a number of interesting questions and directions for future research. This is joint work with Tim Laux. | |
