Equidistributing principles in moving finite element methods

Recently Miller and his co-workers proposed a moving finite element method based on a least squares principle. This was followed by a similar method by the present authors using a Petrov—Galerkin approach. In this paper the two methods are compared. In particular, it is shown that both methods move...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 9; no. 4; pp. 377 - 389
Main Authors Herbst, B.M., Schoombie, S.W., Mitchell, A.R.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.01.1983
Elsevier
Subjects
Burgers' equation
equidistributing principle
Exact sciences and technology
Mathematics
moving finite element method
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Sciences and techniques of general use
equidistributing principle
Burgers' equation
moving finite element method
65M50
Finite element method
Initial value problem
Partial differential equation
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Summary:Recently Miller and his co-workers proposed a moving finite element method based on a least squares principle. This was followed by a similar method by the present authors using a Petrov—Galerkin approach. In this paper the two methods are compared. In particular, it is shown that both methods move their nodes according to an approximate equidistributing principle. This observation leads to a criterion for the placement of the nodes. It is also shown that the penalty function designed by Miller may also be used with the Petrov—Galerkin method. Finally, numerical examples are given, illustrating the performance of the two methods.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0377-0427
1879-1778
DOI:10.1016/0377-0427(83)90009-2