Finite element approximation of a timefractional diffusion problem in a nonconvex polygonal domain
Abstract
An initialboundary value problem for the timefractional diffusion equation is discretized in space using continuous piecewiselinear finite elements on a polygonal domain with a reentrant 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 secondorder accurate if quasiuniform triangulations are used. We prove that a suitable local mesh refinement about the reentrant corner restores secondorder convergence. In this way, we generalize known results for the classical heat equation due to Chatzipantelidis, Lazarov, Thomée and Wahlbin.
 Publication:

arXiv eprints
 Pub Date:
 January 2016
 arXiv:
 arXiv:1602.00040
 Bibcode:
 2016arXiv160200040N
 Keywords:

 Mathematics  Numerical Analysis;
 33E12;
 35D10;
 35R11;
 65N30;
 65N50
 EPrint:
 21 pages, 4 figures