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

被引：7
|
作者：
Le, Kim Ngan [1 ]
Mclean, William [1 ]
Lamichhane, Bishnu [2 ]
机构：
[1] Univ New South Wales, Sch Math & Stat, Sydney, NSW 2052, Australia
[2] Univ Newcastle, Sch Math & Phys Sci, Callaghan, NSW 2308, Australia
来源：
ANZIAM JOURNAL | 2017年 / 59卷 / 01期
关键词：
local mesh refinement; non-smooth initial data; Laplace transformation; EQUATIONS;
D O I：
10.1017/S1446181116000365
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 restores second-order convergence. In this way, we generalize known results for the classical heat equation.
引用
收藏
页码：61 / 82
页数：22
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