Preconditioning and Boundary Conditions without $H_2$ Estimates: $L_2$ Condition Numbers and the Distribution of the Singular Values

DOI10.1137/0730017zbMath0773.65033OpenAlexW2001837653MaRDI QIDQ4695034

Charles I. Goldstein, Seymour V. Parter, Thomas A. Manteuffel

Publication date: 25 October 1993

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0730017

zbMATH Keywords

finite element condition number singular values second order elliptic operators preconditioned operators

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 computation of matrix norms, conditioning, scaling (65F35) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

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Preconditioning isoparametric finite element methods taking into account numerical integration ⋮ Robust Superlinear Krylov Convergence for Complex Noncoercive Compact-Equivalent Operator Preconditioners ⋮ Superlinear PCG Algorithms: Symmetric Part Preconditioning and Boundary Conditions ⋮ Superior properties of the PRESB preconditioner for operators on two-by-two block form with square blocks ⋮ Superlinearly convergent PCG algorithms for some nonsymmetric elliptic systems ⋮ Newton-$\mathrm{LL}^\ast$ method for the second-order semi-linear elliptic partial differential equations ⋮ Preconditioning a class of fourth order problems by operator splitting ⋮ Superlinear Convergence of the GMRES for PDE-Constrained Optimization Problems ⋮ Superlinearly convergent CG methods via equivalent preconditioning for nonsymmetric elliptic operators ⋮ Equivalent operator preconditioning for elliptic problems

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