Work

Error estimates for numerical approximations of a nonlinear gradient flow model

Year: 2026

Type: article

Abstract: We perform numerical analysis of a nonlinear gradient flow, which can be regarded as a parabolic minimal surface problem or a regularised total variation flow, using the gradient discretisation method (GDM). GDM is a unified convergence analysis framework that covers conforming and nonconforming numerical methods, for instance, conforming and nonconforming finite element, two-point flux approximation, etc.. In this paper, a fully discretised implicit scheme of the model is proposed, the existence and uniqueness of the solution to the scheme is proved, the stability and consistency of the scheme are analysed, and error estimates are established. Numerical results based on the conforming and nonconforming P1 finite elements are also provided.

Source: Computers & Mathematics with Applications

DOI: 10.1016/j.camwa.2026.04.009

Authors: Jérôme Droniou, Kim-Ngan Le, Huateng Zhu

Institutions: Centre National de la Recherche Scientifique, Institut Montpelliérain Alexander Grothendieck, Monash University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,170

Funders: Australian Government, Government of Western Australia, Australian Research Council