Smoothers, mesh dependent norms, interpolation and multigrid

New estimates for the nodal interpolation operator for the P 1 finite element are established with respect to mesh dependent norms that are defined in terms of the smoothers in multigrid algorithms. These estimates are useful in the additive approach to the convergence of V-cycle multigrid algorithm...

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Bibliographic Details
Published in:Applied numerical mathematics Vol. 43; no. 1; pp. 45 - 56
Main Author: Brenner, Susanne C.
Format: Journal Article Conference Proceeding
Language:English
Published: Amsterdam Elsevier B.V 01.10.2002
Elsevier
Subjects:
Damped Jacobi
Exact sciences and technology
Finite element
Interpolation estimates
Mathematics
Mesh dependent norms
Multigrid
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Partial differential equations, boundary value problems
Richardson
Sciences and techniques of general use
Symmetric Gauss–Seidel
Mesh dependent norms
Richardson
Multigrid
Symmetric Gauss–Seidel
Interpolation estimates
Damped Jacobi
Finite element
Interpolation formula
Convergence of numerical methods
Estimate
Smoothing methods
Jacobi method
Asymptotic behavior
Algorithm
Partial differential equation
Numerical approximation
Finite element method
Elliptic equation
Boundary value problem
Symmetric model
Mesh dependent norm
Gauss Seidel method
Richardson number
ISSN:0168-9274, 1873-5460
Online Access:Get full text
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Summary:New estimates for the nodal interpolation operator for the P 1 finite element are established with respect to mesh dependent norms that are defined in terms of the smoothers in multigrid algorithms. These estimates are useful in the additive approach to the convergence of V-cycle multigrid algorithms and lead to results on the asymptotic behavior of the contraction numbers with respect to the number of smoothing steps.
ISSN:0168-9274
1873-5460
DOI:10.1016/S0168-9274(02)00117-4