DPG Method with Optimal Test Functions for a Fractional Advection Diffusion Equation |
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| Authors: | Vincent J. Ervin Thomas Führer Norbert Heuer Michael Karkulik |
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| Affiliation: | 1.Department of Mathematical Sciences,Clemson University,Clemson,USA;2.Facultad de Matemáticas,Pontificia Universidad Católica de Chile,Macul,Chile;3.Departamento de Matemática,Universidad Técnica Federico Santa María,Valparaiso,Chile |
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| 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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