Refinement strategies for polygonal meshes applied to adaptive VEM discretization

TL;DR

This paper investigates various adaptive mesh refinement strategies for polygonal meshes in complex geometrical domains, focusing on solution quality and efficiency in discretizing differential problems, with a case study on a geophysical application.

Contribution

It introduces and compares different refinement strategies for polygonal meshes, analyzing their optimality and reliability in adaptive virtual element method discretizations.

Findings

Refinement strategies improve mesh quality and solution accuracy.

Optimality depends on the number of degrees of freedom.

Strategies are effective in complex geophysical problems.

Abstract

In the discretization of differential problems on complex geometrical domains, discretization methods based on polygonal and polyhedral elements are powerful tools. Adaptive mesh refinement for such kind of problems is very useful as well and states new issues, here tackled, concerning good quality mesh elements and reliability of the simulations. In this paper we numerically investigate optimality with respect to the number of degrees of freedom of the numerical solutions obtained by the different refinement strategies proposed. A geometrically complex geophysical problem is used as test problem for several general purpose and problem dependent refinement strategies.