A Second Order Time Accurate SUSHI Method for the Time-Fractional Diffusion Equation
SUSHI (Scheme Using Stabilization and Hybrid Interfaces) is a finite volume method developed at the first time to approximate heterogeneous and anisotropic diffusion problems. It has been applied later to approximate several types of partial differential equations. The formulation of SUSHI involves a consistent and stable Discrete Gradient which is developed for a large class of nonconforming meshes in any space dimension.
In this note, we establish a second order time accurate implicit scheme for the Time Fractional Diffusion Equation. The space discretization is based on the use of SUSHI whereas the time discretization is performed using a uniform mesh. We state and prove a discrete a priori estimate from which we derive an optimal convergence order in \(L^\infty (L^2)\).
KeywordsTime fractional diffusion equation SUSHI scheme Discrete gradient Second order implicit scheme