Moving finite element methods for evolutionary problems. II. Applications

In this, the second of two papers on the subject, we present applications of the moving finite element method to a number of test problems. Key features are linear elements, a direct approach to parallelism and node overtaking (avoiding penalty functions), rapid inversion of the mass matrix by preco...

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Published inJournal of computational physics Vol. 79; no. 2; pp. 270 - 297
Main Authors Johnson, I.W, Wathen, A.J, Baines, M.J
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 01.12.1988
Elsevier
Subjects
Exact sciences and technology
Mathematics
Sciences and techniques of general use
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ISSN0021-9991
1090-2716
DOI10.1016/0021-9991(88)90017-4

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Summary:In this, the second of two papers on the subject, we present applications of the moving finite element method to a number of test problems. Key features are linear elements, a direct approach to parallelism and node overtaking (avoiding penalty functions), rapid inversion of the mass matrix by preconditioned conjugate gradients, and explicit Euler time stepping. The resulting codes are fast and efficient and are able to follow fronts and similar features with great accuracy. The paper includes a substantial section on changes of dependent variable and front tracking techniques for non-linear diffusion problems. Test problems include non-linear hyperbolic conservation laws and non-linear parabolic equations in one and two dimensions.
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ISSN:0021-9991
1090-2716
DOI:10.1016/0021-9991(88)90017-4