A Coarsening Algorithm on Adaptive Red-Green-Blue Refined Meshes

01/17/2020
by   Stefan A. Funken, et al.
0

Adaptive meshing is a fundamental component of adaptive finite element methods. This includes refining and coarsening meshes locally. In this work, we are concerned with the red-green-blue refinement strategy and its counterpart - coarsening. In general, coarsening algorithms are mostly based on an explicitly given refinement history. In this work, we present a coarsening algorithm on adaptive red-green-blue meshes without explicitly knowing the refinement history. To this end, we examine the local structure of these meshes, find an easy-to-verify criterion to coarsen red-green-blue meshes and prove that this criterion generates meshes with the desired properties. However, it does not guarantee that the set of nodes admissible for coarsening is non-empty. Therefore, we also present an additional algorithm that uses the main ideas of this criterion to always allow for local coarsening. We present a MATLAB implementation built on the red-green-blue refinement routine of the ameshref-package.

READ FULL TEXT

Authors

page 16

page 17

11/04/2020

Local Coarsening Algorithms on Adaptively Refined Meshes in 2D and Their Efficient Implementation in MATLAB

Adaptive meshing includes local refinement as well as coarsening of mesh...
01/10/2021

Implementation of Polygonal Mesh Refinement in MATLAB

We present a simple and efficient MATLAB implementation of the local ref...
08/28/2020

H^1-Stability of the L^2-Projection onto Finite Element Spaces on Adaptively Refined Quadrilateral Meshes

The L^2-orthogonal projection Π_h:L^2(Ω)→𝕍_h onto a finite element (FE) ...
09/30/2021

The Scott-Vogelius Method for Stokes Problem on Anisotropic Meshes

This paper analyzes the Scott-Vogelius divergence-free element pair on a...
03/07/2019

An adaptive strategy based on conforming quadtree meshes for kinematic limit analysis

We propose a simple and efficient scheme based on adaptive finite elemen...
09/18/2019

Layer-adapted meshes: Milestones in 50 years of history

50 years ago the first paper on layer-adapted meshes appeared. We sketch...
12/31/2019

Near-best adaptive approximation on conforming meshes

We devise a generalization of tree approximation that generates conformi...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.