DPG method with optimal test functions for a fractional advection diffusion equation
Provides a rigorous numerical framework for solving fractional advection-diffusion problems, which are important in modeling anomalous transport phenomena.
Developed a DPG method with optimal test functions for a fractional advection diffusion equation, proving well-posedness and quasi-optimal convergence, with numerical experiments confirming convergence on uniform and adaptive meshes.
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.