Abstract
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 -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. In this way, we generalize known results for the classical heat equation.
Original language | English |
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Pages (from-to) | 61-82 |
Number of pages | 22 |
Journal | The ANZIAM Journal |
Volume | 59 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Jul 2017 |
Externally published | Yes |
Keywords
- Laplace transformation
- local mesh refinement
- non-smooth initial data