Hierarchical bases of finite-element spaces in the discretization of nonsymmetric elliptic boundary value problems

DOI10.1007/BF02240145zbMath0566.65080OpenAlexW61054527MaRDI QIDQ1059379

Harry Yserentant

Publication date: 1985

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02240145

zbMATH Keywords

numerical examplesmultigrid methodsfast solversfinite element spacesKrylov-space methodsspectral condition numbersconjugate gradient type methodsHierarchical bases

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items (8)

The hierarchical basis multigrid method ⋮ Preconditioners for Krylov subspace methods: An overview ⋮ A note on the complexity of solving Poisson's equation for spaces of bounded mixed derivatives ⋮ The hierarchical basis multigrid method for convection-diffusion equations ⋮ Electromagnetic device modeling using a new adaptive wavelet finite element method ⋮ Hierarchical bases give conjugate gradient type methods a multigrid speed of convergence ⋮ Mesh independence of galerkin approach by preconditioning ⋮ Incomplete block matrix factorization preconditioning methods. The ultimate answer?

Cites Work

• Unnamed Item
• Conjugate gradient type methods for unsymmetric and inconsistent systems of linear equations
• Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods
• On the convergence of multi-level methods for strongly nonuniform families of grids and any number of smoothing steps per level
• Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
• Practical Use of Some Krylov Subspace Methods for Solving Indefinite and Nonsymmetric Linear Systems
• Krylov Subspace Methods for Solving Large Unsymmetric Linear Systems
• The Lanczos Biorthogonalization Algorithm and Other Oblique Projection Methods for Solving Large Unsymmetric Systems

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