Implicit extrapolation methods for variable coefficient problems

Implicit extrapolation methods for the solution of partial differential equations are based on applying the extrapolation principle indirectly. Multigrid $\tau$-extrapolation is a special case of this idea. In the context of multilevel finite element methods, an algorithm of this type can be used to...

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Bibliographic Details
Published inSIAM journal on scientific computing Vol. 19; no. 4; pp. 1109 - 1124
Main Authors JUNG, M, RÜDE, U
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Society for Industrial and Applied Mathematics 01.07.1998
Subjects
Algorithms
Approximation
Boundary conditions
Boundary value problems
Exact sciences and technology
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Partial differential equations, boundary value problems
Sciences and techniques of general use
Finite element method
Extrapolation
Stiffness matrix
Numerical integration
Boundary value problem
Multilevel method
Multigrid
Implicit extrapolation method
Partial differential equation
Convergence
Romberg integration method
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Summary:Implicit extrapolation methods for the solution of partial differential equations are based on applying the extrapolation principle indirectly. Multigrid $\tau$-extrapolation is a special case of this idea. In the context of multilevel finite element methods, an algorithm of this type can be used to raise the approximation order, even when the meshes are nonuniform or locally refined. The implicit extrapolation multigrid algorithm converges to the solution of a higher order finite element system. This is obtained without explicitly constructing higher order stiffness matrices but by applying extrapolation in a natural form within the algorithm. The algorithm requires only a small change of a basic low order multigrid method.
ISSN:1064-8275
1095-7197
DOI:10.1137/S1064827595293557