FINITE ELEMENT APPROXIMATION OF A TIME-FRACTIONAL DIFFUSION PROBLEM FOR A DOMAIN WITH A RE-ENTRANT CORNER

@article{Le2017FINITEEA,
  title={FINITE ELEMENT APPROXIMATION OF A TIME-FRACTIONAL DIFFUSION PROBLEM FOR A DOMAIN WITH A RE-ENTRANT CORNER},
  author={Kim-Ngan Le and William McLean and Bishnu P. Lamichhane},
  journal={The ANZIAM Journal},
  year={2017},
  volume={59},
  pages={61 - 82}
}
An initial-boundary value problem for a time-fractional diffusion equation is discretized in space, using continuous piecewise-linear finite elements on a domain with a re-entrant corner. Known error bounds for the case of a convex domain 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… Expand
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