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DPG method with optimal test functions for a fractional advection diffusion equation (1507.06691v1)
Published 23 Jul 2015 in math.NA
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.