Accurate numerical resolution of transients in initial-boundary value problems for the heat equation

被引：31

作者：

Flyer, N ^{[1
]}

Fornberg, B ^{[1
]}

机构：

[1] Univ Colorado, Dept Math Appl, Boulder, CO 80309 USA

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2003年 / 184卷 / 02期

关键词：

PDE; initial-boundary value problem; corner singularity; heat equation; Chebyshev method;

D O I：

10.1016/S0021-9991(02)00034-7

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

If the initial and boundary data for a PDE do not obey an infinite set of compatibility conditions, singularities will arise in the solution at the corners of the initial time-space domain. For dissipative equations, such as the 1-D heat equation or 1-D convection-diffusion equations, the impacts of these singularities are short lived. However, they can cause a very severe loss of numerical accuracy if we are interested in transient solutions. The phenomenon has been described earlier from a theoretical standpoint. Here, we illustrate it graphically and present a simple remedy which, with only little extra cost and effort, restores full numerical accuracy. (C) 2002 Elsevier Science B.V. All rights reserved.

引用

页码：526 / 539

页数：14

共 7 条

[1] Compatibility conditions for time-dependent partial differential equations and the rate of convergence of Chebyshev and Fourier spectral methods [J].