Work

Dynamic Ritz Projection of Mean Curvature Flow and Optimal \(\boldsymbol{L^2}\) Convergence of Parametric FEM

Year: 2025

Type: article

Abstract: . A new approach is developed to study the convergence of parametric finite element approximations to the mean curvature flow of closed surfaces in three-dimensional space. In this approach, the error analysis is conducted by comparing the numerical solution to a dynamic Ritz projection of the mean curvature flow introduced in this paper rather than an interpolation of the mean curvature flow, as commonly used in the literature. The errors associated with the dynamic Ritz projection in approximating the mean curvature flow are established in the [Formula: see text] and [Formula: see text] norms. Leveraging these results, optimal-order convergence of parametric finite element methods for mean curvature flow of closed surfaces in the [Formula: see text] norm is proved, including the convergence of parametric finite element methods with piecewise linear finite elements.

Source: SIAM Journal on Numerical Analysis

DOI: 10.1137/24m1689053

Authors: Buyang Li, Rong Tang

Institution: Hong Kong Polytechnic University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funder: Hong Kong Polytechnic University

Awards: G5121381557, G6840077960, G7967431948