New metric tensors for anisotropic mesh generation

TL;DR

This paper introduces a novel anisotropic mesh adaptation strategy using a new metric tensor that improves accuracy and efficiency in finite element solutions of elliptic PDEs, especially for complex 2D problems.

Contribution

It proposes a new metric tensor for anisotropic mesh generation that leverages comprehensive anisotropy information, enhancing mesh adaptation accuracy over existing methods.

Findings

Improved accuracy in finite element solutions for elliptic equations.

Enhanced efficiency in mesh generation for complex 2D problems.

Successful application to Poisson and convection-dominated problems.

Abstract

A new anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in some metric space, with the metric tensor being computed based on a posteriori error estimates proposed in \cite{YinXie}. The new metric tensor explores more comprehensive information of anisotropy for the true solution than those existing ones. Numerical results show that this approach can be successfully applied to deal with poisson and steady convection-dominated problems. The superior accuracy and efficiency of the new metric tensor to others is illustrated on various numerical examples of complex two-dimensional simulations.