Moving Mesh Techniques Based upon Equidistribution, and Their Stability

Various aspects of the moving mesh problem are investigated for the solution of partial differential equations (PDEs) in one space dimension. In particular, methods based (explicitly or implicitly) upon an equidistribution principle are studied. It is shown that equidistribution implicitly correspon...

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Bibliographic Details
Published in:SIAM journal on scientific and statistical computing Vol. 13; no. 6; pp. 1265 - 1286
Main Authors: Ren, Yuhe, Russell, Robert D.
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.11.1992
Subjects:
Exact sciences and technology
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Partial differential equations
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Sciences and techniques of general use
One dimensional space
Grid pattern
Burgers equation
Reaction diffusion equation
Partial differential equation
Numerical stability
ISSN:0196-5204, 1064-8275, 2168-3417, 1095-7197
Online Access:Get full text
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Summary:Various aspects of the moving mesh problem are investigated for the solution of partial differential equations (PDEs) in one space dimension. In particular, methods based (explicitly or implicitly) upon an equidistribution principle are studied. It is shown that equidistribution implicitly corresponds to finding a solution to a PDE involving a new set of computational coordinates. Implementation of a discrete version of equidistribution to compute a moving mesh corresponds to solving a weak form of the PDE. The stability of equidistribution is discussed, and it is argued that stability can be significantly affected by the way in which this solution process is carried out. Simple moving mesh methods are constructed using this framework, and numerical examples are given to illustrate their robustness.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0196-5204
1064-8275
2168-3417
1095-7197
DOI:10.1137/0913072