A comparative numerical study of meshing functionals for variational mesh adaptation

TL;DR

This paper compares three different functionals used for variational mesh adaptation, analyzing their effectiveness in 2D and 3D through numerical experiments focused on mesh quality.

Contribution

It provides a comparative numerical analysis of three functionals for variational mesh adaptation, including a generalization of Winslow's functional.

Findings

All three functionals perform well in mesh adaptation tasks.

The study highlights differences in mesh quality measures among the functionals.

Numerical results demonstrate the effectiveness of each functional in 2D and 3D.

Abstract

We present a comparative numerical study for three functionals used for variational mesh adaptation. One of them is a generalisation of Winslow's variable diffusion functional while the others are based on equidistribution and alignment. These functionals are known to have nice theoretical properties and work well for most mesh adaptation problems either as a stand-alone variational method or combined within the moving mesh framework. Their performance is investigated numerically in terms of equidistribution and alignment mesh quality measures. Numerical results in 2D and 3D are presented.