Temporal Derivatives in the Finite-Element Method on Continuously Deforming Grids

When solving certain time-dependent partial differential equations using a finite-element technique on a deforming grid, it is shown that there is a need to differentiate the trial solution with respect to the position of each of the moveable node points. A result is presented which enables these no...

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Bibliographic Details
Published inSIAM journal on numerical analysis Vol. 28; no. 4; pp. 990 - 1003
Main Authors Jimack, P. K., Wathen, A. J.
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Society for Industrial and Applied Mathematics 01.08.1991
Subjects
Coordinate systems
Exact sciences and technology
Finite element analysis
Finite element method
Mathematical functions
Mathematical theorems
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations
Sciences and techniques of general use
Vertices
Finite element method
Topology
Boundary condition
Partial differential equation
Trial function
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Summary:When solving certain time-dependent partial differential equations using a finite-element technique on a deforming grid, it is shown that there is a need to differentiate the trial solution with respect to the position of each of the moveable node points. A result is presented which enables these nonstandard derivatives to be expressed in terms of the standard spatial derivatives of the trial functions provided that certain conditions are satisfied. These conditions are investigated and shown to be satisfied for a large class of trial spaces. Even when the necessary conditions are not satisfied by all of the trial functions being used, the result is shown to be still of great use in evaluating these awkward nodal derivatives.
ISSN:0036-1429
1095-7170
DOI:10.1137/0728052