Work

Adaptive Mesh Refinement for Arbitrary Initial Triangulations

Year: 2025

Type: article

Abstract: We introduce a simple initialization of the Maubach bisection routine for adaptive mesh refinement which applies to any conforming initial triangulation and terminates in linear time with respect to the number of initial vertices. We show that Maubach’s routine with this initialization always terminates and generates meshes that preserve shape regularity and satisfy the closure estimate needed for optimal convergence of adaptive schemes. Our ansatz allows for the intrinsic use of existing implementations.

Source: Foundations of Computational Mathematics

DOI: 10.1007/s10208-025-09698-7

Authors: Lars Diening, Lukas Gehring, Johannes Storn

Institutions: Bielefeld University, Friedrich Schiller University Jena, Leipzig University

Language: English

Topic: Computational Geometry and Mesh Generation

Subfield: Computer Graphics and Computer-Aided Design

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,290

Funders: European Commission, Deutsche Forschungsgemeinschaft, Universität Bielefeld