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

页码：61 / 82

页数：22

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