Abstract

DPG method with optimal test functions for a fractional advection diffusion equation

Vincent J. Ervin, Thomas Führer, Norbert Heuer, and Michael Karkulik
J. Sci. Comput. 72 (2), 568-585, 2017.

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.