MOVCOL4: A moving mesh code for fourth-order time-dependent partial differential equations

被引：19
|
作者：
Russell, R. D. [1 ]
Williams, J. F. [1 ]
Xu, X. [1 ]
机构：
[1] Simon Fraser Univ, Dept Math, Burnaby, BC V5A 1S6, Canada
来源：
SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2007年 / 29卷 / 01期
关键词：
moving mesh methods; collocation discretization; adaptive numerical methods; finite-time singularities; blow-up; pinch-off; thin-film equation; higher-order equations;
D O I：
10.1137/050643167
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we develop and analyze a moving mesh code for the adaptive simulation of fourth-order PDEs based on collocation. The scheme is shown to enforce discrete conservation for problems written in a generalized conservation form. To demonstrate the breadth of applicability we present examples from both Cahn-Hilliard and thin-film-type equations exhibiting metastable behavior, finite-time solution blow-up, finite-time extinction, and moving interfaces.
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页码：197 / 220
页数：24
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