Optimal approximation spaces for discontinuous Petrov-Galerkin finite element methods

arXiv (Cornell University)

Abstract

Certain Petrov-Galerkin schemes are inherently stable formulations of variational problems on a given mesh. This stability is primarily obtained by computing an optimal test basis for a given approximation space. Furthermore, these Petrov-Galerkin schemes are equipped with a robust a posteriori error estimate which makes them an ideal candidate for mesh adaptation. One could extend these Petrov-Galerkin schemes not only to have optimal test spaces but also optimal approximation spaces with respect to current estimates of the solution. These extensions are the main focus of this article. In this article, we provide a methodology to drive mesh adaptation to produce optimal meshes for resolving solution features and output functionals which we demonstrate through numerical experiments.

Authors 3

1. Ankit Chakraborty Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University

2. Ajay Mandyam Rangarajan Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University

3. Georg May

   Von Karman Institute for Fluid Dynamics

   Affiliation as printed

   von Karman Institute For Fluid Dynamics