COMPACTNESS PROPERTIES OF THE DG AND CG TIME STEPPING SCHEMES FOR PARABOLIC EQUATIONS

For a broad class of parabolic equations it is shown that numerical solutions computed using the discontinuous Galerkin or the continuous Galerkin time stepping schemes of arbitrary order will inherit the compactness properties of the underlying equation. Convergence of numerical schemes for a phase...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 2010-01, Vol.47 (6), p.4680-4710
Main Author: WALKINGTON, NOEL J.
Format: Article
Language:English
Subjects:
A priori knowledge
Approximation
Banach space
Computational fluid dynamics
Convergence
Embeddings
Exact sciences and technology
Fluid flow
Fluids
Galerkin methods
Hilbert spaces
Hypotheses
Integers
Mathematical analysis
Mathematical discontinuity
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical schemes
Partial differential equations
Sciences and techniques of general use
Topological compactness
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Summary:For a broad class of parabolic equations it is shown that numerical solutions computed using the discontinuous Galerkin or the continuous Galerkin time stepping schemes of arbitrary order will inherit the compactness properties of the underlying equation. Convergence of numerical schemes for a phase field approximation of the flow of two fluids with surface tension is presented to illustrate these results.
ISSN:0036-1429
1095-7170
DOI:10.1137/080728378