A Novel Deformation Method for Higher Order Mesh Generation

TL;DR

This paper introduces a new deformation-based algorithm that combines local refinement to generate higher order meshes, improving mesh adaptation for finite element methods in 2D and 3D.

Contribution

It presents a novel deformation method integrated with local refinement specifically for higher order mesh generation, extending existing mesh adaptation techniques.

Findings

Effective in 2D and 3D for p=3 meshes

Prescribed positive Jacobian determinant achieved

Demonstrated through numerical examples

Abstract

The development of higher order finite elements methods has become an active research area. The deformation method for mesh generation has achieved a prescribed positive Jacobian determinant constraint and it has been a useful method for mesh adaptation. In this work, the deformation method is combined with local refinement to generate higher order meshes. 2D and 3D numerical examples of element order p=3 are shown to demonstrate the effectiveness of our new algorithm.