Self-similar numerical solutions of the porous-medium equation using moving mesh methods

被引：23

作者：

Budd, CJ

Collins, GJ

Huang, WZ

Russell, RD

机构：

[1] Univ Bath, Dept Math, Bath BA2 7AY, Avon, England

[2] Univ Bristol, Sch Math, Bristol BS8 1TW, Avon, England

[3] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

[4] Simon Fraser Univ, Burnaby, BC V5A 1S6, Canada

来源：

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 1999年 / 357卷 / 1754期

关键词：

porous-medium equation; self-similar solution; Lie-group invariance; conservation laws; mesh adaptation; equidistribution;

D O I：

10.1098/rsta.1999.0364

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

This paper examines a synthesis of adaptive mesh methods with the use of symmetry to study a partial differential equation. In particular, it considers methods which admit discrete self-similar solutions, examining the convergence of these to the true self-similar solution as well as their stability. Special attention is given to the nonlinear diffusion equation describing flow in a porous medium.

引用

页码：1047 / 1077

页数：31

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