Extending h adaptivity with refinement patterns

TL;DR

This paper introduces a systematic approach to generate optimal meshes in finite element analysis by using a library of refinement patterns, applicable to any element type, enhancing adaptivity and mesh quality.

Contribution

It presents a novel methodology for integrating refinement patterns into h adaptive FEM codes, allowing flexible and optimal mesh generation for complex geometries.

Findings

Effective mesh refinement for complex geometries

Flexible pattern library for various element types

Improved mesh quality and adaptivity

Abstract

This contribution introduces the idea of refinement patterns for the generation of optimal meshes in the context of the Finite Element Method. The main idea is to generate a library of possible patterns on which elements can be refined and use this library to inform an h adaptive code on how to handle complex refinements in regions of interest. There are no restrictions on the type of elements that can be refined, and the patterns can be generated for any element type. The main advantage of this approach is that it allows for the generation of optimal meshes in a systematic way where, even if a certain pattern is not available, it can easily be included through a simple text file with nodes and sub-elements. The contribution presents a detailed methodology for incorporating refinement patterns into h adaptive Finite Element Method codes and demonstrates the effectiveness of the approach through mesh refinement of problems with complex geometries.