The discontinuous Galerkin method for fractional degenerate convection-diffusion equations
Provides theoretical and numerical foundations for solving a class of fractional PDEs, but the results are incremental within the numerical analysis domain.
The paper develops discontinuous Galerkin methods for fractional degenerate convection-diffusion equations, proving stability and convergence to entropy solutions, with numerical experiments illustrating solution behavior.
We propose and study discontinuous Galerkin methods for strongly degenerate convection-diffusion equations perturbed by a fractional diffusion (Lévy) operator. We prove various stability estimates along with convergence results toward properly defined (entropy) solutions of linear and nonlinear equations. Finally, the qualitative behavior of solutions of such equations are illustrated through numerical experiments.