Multigrid convergence for nonsymmetric, indefinite variational problems and one smoothing step

DOI10.1016/0096-3003(86)90104-9zbMath0614.65031OpenAlexW2060615213MaRDI QIDQ1819888

Jan Mandel

Publication date: 1986

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0096-3003(86)90104-9

zbMATH Keywords

convergenceHilbert spacemultigrid methodbilinear formsymmetric positive definiteindefinitenonsymmetricV-cyclesRichards iteration

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Variational methods for second-order elliptic equations (35J20) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items (14)

A preconditioned GMRES method ⋮ Convergence of multigrid methods for nonsymmetric, indefinite problems ⋮ A multigrid method for a parameter dependent problem in solid mechanics ⋮ The analysis of PMHSS-multigrid methods for elliptic problems with smooth complex coefficients ⋮ Multigrid method as an accelerating procedure for solving systems of linear algebraic equations with a dissipative matrix ⋮ Convergence analysis of HSS-multigrid methods for second-order nonselfadjoint elliptic problems ⋮ A survey of multilevel preconditioned iterative methods ⋮ Multigrid methods with PSTS- and HSS-smoothers for solving the unsteady Navier-Stokes equations ⋮ Iterative Schemes for Nonsymmetric and Indefinite Elliptic Boundary Value Problems ⋮ Norm estimates of product operators with application to domain decomposition ⋮ Fourier analysis of multigrid for a model two-dimensional convection-diffusion equation ⋮ The Analysis of Multigrid Algorithms for Nonsymmetric and Indefinite Elliptic Problems ⋮ Multigrid method for solving convection-diffusion problems with dominant convection ⋮ Unnamed Item

Cites Work

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• The contraction number of a multigrid method with mesh ratio 2 for solving Poisson's equation
• Algebraic study of multigrid methods for symmetric, definite problems
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• Multigrid Methods for Variational Problems: Further Results
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• A New Convergence Proof for the Multigrid Method Including the V-Cycle
• Sharp Estimates for Multigrid Rates of Convergence with General Smoothing and Acceleration
• Multigrid Methods for Variational Problems: General Theory for the V-Cycle
• An Algebraic Theory for Multigrid Methods for Variational Problems
• An Optimal Order Process for Solving Finite Element Equations
• A Comparison of Two Multilevel Iterative Methods for Nonsymmetric and Indefinite Elliptic Finite Element Equations
• On the l 2 Convergence of an Algorithm for Solving Finite Element Equations
• On Multigrid Convergence in the Indefinite Case

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