Finite element approximation of a time-fractional diffusion problem for a doman with a re-entrant corner

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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