Near-best adaptive approximation on conforming meshes

TL;DR

This paper introduces a generalized tree approximation method for conforming meshes, achieving near-best approximation independent of certain constants, with numerical experiments showing improved approximation over previous methods.

Contribution

It presents a novel approach to conforming mesh approximation that ensures near-optimal results without dependence on specific constants like the completion constant.

Findings

Achieves near-best approximation on conforming meshes

Numerical experiments show improved approximation properties

Method is independent of the completion constant for newest-vertex bisection

Abstract

We devise a generalization of tree approximation that generates conforming meshes, i.e., meshes with a particular structure like edge-to-edge triangulations. A key feature of this generalization is that the choices of the cells to be subdivided are affected by that particular structure. As main result, we prove near best approximation with respect to conforming meshes, independent of constants like the completion constant for newest-vertex bisection. Numerical experiments complement the theoretical results and indicate better approximation properties than previous approaches.