Abstract
This work describes a concise algorithm for the generation of triangular meshes with the help of standard adaptive finite element methods. We demonstrate that a generic adaptive finite element solver can be repurposed into a triangular mesh generator if a robust mesh smoothing algorithm is applied between the mesh refinement steps. We present an implementation of the mesh generator and demonstrate the resulting meshes via examples.
Highlights
Many numerical methods for partial differential equations (PDE’s), such as the finite element method (FEM) and the finite volume method (FVM), are based on splitting the domain of the solution into primitive shapes such as triangles or tetrahedra
The collection of the primitive shapes, i.e. the computational mesh, is used to define the discretisation, e.g., in the FEM, the shape functions are polynomial in each mesh element, and in the FVM, the discrete fluxes are defined over the cell edges or faces
This article describes a simple approach for the triangulation of two-dimensional polygonal domains
Summary
Many numerical methods for partial differential equations (PDE’s), such as the finite element method (FEM) and the finite volume method (FVM), are based on splitting the domain of the solution into primitive shapes such as triangles or tetrahedra. It is noteworthy that the steps 2, 3 and 5 correspond exactly to what is done in any implementation of the standard adaptive FEM; cf Verfürth [21] who calls it the adaptive process. The goal of this work is to demonstrate that if the mesh smoothing algorithm of step 4 is chosen properly, the adaptive process tends to produce reasonable meshes even if the initial mesh is of low quality. We demonstrate that the adaptive process—together with an implementation of the CDT and a robust mesh smoothing algorithm—can act as a simple triangular mesh generator
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