hp-FEM for the fractional heat equation
Jens Markus Melenk, Alexander Rieder · IMA Journal of Numerical Analysis · 2020
Abstract We consider a time-dependent problem generated by a nonlocal operator in space. Applying for the spatial discretization a scheme based on $hp$-finite elements and a Caffarelli–Silvestre extension we obtain a semidiscrete semigroup. The discretization in time is carried out by using $hp$-discontinuous Galerkin based time stepping. We prove exponential convergence for such a method in an abstract framework for the discretization in the spatial domain $\varOmega $.