DPG method with optimal test functions for a fractional advection diffusion equation
Numerical Analysis
2015-07-27 v1
Abstract
We develop an ultra-weak variational formulation of a fractional advection diffusion problem in one space dimension and prove its well-posedness. Based on this formulation, we define a DPG approximation with optimal test functions and show its quasi-optimal convergence. Numerical experiments confirm expected convergence properties, for uniform and adaptively refined meshes.
Cite
@article{arxiv.1507.06691,
title = {DPG method with optimal test functions for a fractional advection diffusion equation},
author = {Vincent J. Ervin and Thomas Führer and Norbert Heuer and Michael Karkulik},
journal= {arXiv preprint arXiv:1507.06691},
year = {2015}
}