A Discontinuous Petrov--Galerkin Method for Time-Fractional Diffusion Equations
A Discontinuous Petrov--Galerkin Method for Time-Fractional Diffusion Equations
We propose and analyze a time-stepping discontinuous Petrov--Galerkin method combined with the continuous conforming finite element method in space for the numerical solution of time-fractional subdiffusion problems. We prove the existence, uniqueness, and stability of approximate solutions and derive error estimates. To achieve high order convergence rates from the time …