A Direct Discontinuous Galerkin Method for Time Fractional Diffusion Equations with Fractional Dynamic Boundary Conditions (Journal of Computational Mathematics, 2023)
This paper deals with the numerical approximation for the time fractional diffusionproblem with fractional dynamic boundary conditions. The well-posedness for the weaksolutions is studied. A direct discontinuous Galerkin approach is used in spatial directionunder the uniform meshes, together with a second-order Alikhanov scheme is utilized intemporal direction on the graded mesh, and then the fully discrete scheme is constructed.Furthermore, the stability and the error estimate for the full scheme are analyzed in detail.Numerical experiments are also given to illustrate the effectiveness of the proposed method.