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

2015/07/23 by Ervin, Vincent J., Führer, Thomas, Heuer, Norbert +1
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1507.06691

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.

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