A convergence theory of multilevel additive Schwarz methods on unstructured meshes

DOI10.1007/BF02207701zbMath0872.65097OpenAlexW2063228755WikidataQ57397395 ScholiaQ57397395MaRDI QIDQ676937

Jun Zou, Tony F. Chan

Publication date: 20 October 1997

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02207701

zbMATH Keywords

convergenceunstructured meshesdomain decomposition methodspreconditionerscondition number boundsmultilevel additive Schwarz methodsnon-selfadjoint parabolic problems

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Boundary value problems for second-order elliptic equations (35J25) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Initial value problems for second-order parabolic equations (35K15) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55)

Related Items (14)

A regularized domain decomposition method with Lagrange multiplier ⋮ Parallel algebraic multilevel Schwarz preconditioners for a class of elliptic PDE systems ⋮ Convergence analysis of finite element methods for \(H\) (curl; \(\Omega \))-elliptic interface problems ⋮ Explicit/implicit and Crank-Nicolson domain decomposition methods for parabolic partial differential equations ⋮ Multilevel Schwarz methods for elliptic partial differential equations ⋮ Analysis of the SORAS domain decomposition preconditioner for non-self-adjoint or indefinite problems ⋮ Domain decomposition methods for linear and semilinear elliptic stochastic partial differential equations ⋮ The mortar element method for nonselfadjoint parabolic problem ⋮ Auxiliary space preconditioning in \(H_0(\text{curl};\Omega)\) ⋮ Convergence analysis of finite element methods for H(div;Ω)-elliptic interface problems ⋮ Continuous analysis of the additive Schwarz method: A stable decomposition inH¹with explicit constants ⋮ Numerical methods for elliptic inverse problems ⋮ Construction of explicit extension operators on general finite element grids ⋮ Multiscale domain decomposition methods for elliptic problems with high aspect ratios

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