An exponentially convergent discretization for space–time fractional parabolic equations using 𝘩𝘱-FEM

Abstract

We consider a space–time fractional parabolic problem. Combining a sinc quadrature-based method for discretizing the Riesz–Dunford integral with 𝘩𝘱-FEM in space yields an exponentially convergent scheme for the initial boundary value problem with homogeneous right-hand side. For the inhomogeneous problem, an 𝘩𝘱-quadrature scheme is implemented. We rigorously prove exponential convergence with focus on small times 𝘵⁠, proving robustness with respect to startup singularities due to data incompatibilities.