- Title
- Finite element approximation of a time-fractional diffusion problem for a doman with a re-entrant corner
- Creator
- Le, Kim Ngan; McLean, William; Lamichhane, Bishnu
- Relation
- ANZIAM Journal Vol. 59, Issue 1, p. 61-82
- Publisher Link
- http://dx.doi.org/10.1017/S1446181116000365
- Publisher
- Cambridge University Press
- Resource Type
- journal article
- Date
- 2017
- Description
- 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.
- Subject
- local mesh refinement; non-smooth initial data; Laplace transformation
- Identifier
- http://hdl.handle.net/1959.13/1396760
- Identifier
- uon:34113
- Identifier
- ISSN:1446-1811
- Language
- eng
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