Higher-order meshing of implicit geometries - part III: Conformal Decomposition FEM (CDFEM)

TL;DR

This paper introduces a higher-order finite element method called CDFEM that automatically generates conforming meshes from implicit geometries, achieving optimal accuracy and convergence in complex 2D and 3D problems.

Contribution

The paper presents a novel conformal decomposition finite element method (CDFEM) that automates mesh generation from implicit level-set data with adaptivity for higher-order accuracy.

Findings

Achieves higher-order accuracy with optimal convergence rates.

Successfully decomposes cut elements into conforming sub-elements.

Demonstrates effectiveness in 2D and 3D geometries.

Abstract

A higher-order accurate finite element method is proposed which uses automatically generated meshes based on implicit level-set data for the description of boundaries and interfaces in two and three dimensions. The method is an alternative for fictitious domain and extended finite element methods. The domain of interest is immersed in a background mesh composed by higher-order elements. The zero-level sets are identified and meshed followed by a decomposition of the cut background elements into conforming sub-elements. Adaptivity is a crucial ingredient of the method to guarantee the success of the mesh generation. It ensures the successful decomposition of cut elements and enables improved geometry descriptions and approximations. It is confirmed that higher-order accurate results with optimal convergence rates are achieved with the proposed conformal decomposition finite element method (CDFEM).