In this talk, an initial-boundary value problem for a time-fractional diffusion equation is discretized in space using continuous piecewise-linear finite elements on a polygonal domain with a re-entrant corner. Known error bounds for the case of a convex polygon break down because the associated Poisson equation is no longer $H^2$-regular. In particular, the method is no longer second-order accurate if quasi-uniform triangulations are used. We prove that a suitable local mesh refinement about the re-entrant corner restores second-order convergence.

Dr. Kim Ngan Le obtained her PhD in Applied Mathematics at the University of New South Wales in 2014. She is a postdoctoral fellow in the School of Mathematics and Statistics, the University of New South Wales. Her research interests are numerical methods for fractional PDEs, stochastic (deterministic) nonlinear PDEs.