Two-Level Schwarz Methods for the Biharmonic Problem Discretized Conforming $C^1 $ Elements

DOI10.1137/0733029zbMath0856.65133OpenAlexW2080038010MaRDI QIDQ4880224

Xuejun Zhang

Publication date: 11 February 1997

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

Full work available at URL: https://doi.org/10.1137/0733029

zbMATH Keywords

domain decompositionfinite elementcondition numberbiharmonic Dirichlet problemadditive Schwarz methods

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Boundary value problems for higher-order elliptic equations (35J40) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30)

Related Items (13)

Isogeometric Schwarz preconditioners for the biharmonic problem ⋮ A Two-Level Additive Schwarz Domain Decomposition Preconditioner for a Flat-Top Partition of Unity Method ⋮ Local Multilevel Methods with Rectangular Finite Elements for the Biharmonic Problem ⋮ Two-level additive Schwarz methods for discontinuous Galerkin approximations of the biharmonic equation ⋮ A two-level Schwarz method for a finite element approximation of a nonlinear biharmonic equation. ⋮ An optimal multilevel method with one smoothing step for the Morley element ⋮ Extension theorems for plate elements with applications ⋮ Approximation technics for an unsteady dynamic Koiter shell ⋮ Numerical methods for the rosenau equation ⋮ Preconditioning high order \(H^2\) conforming finite elements on triangles ⋮ A two-level additive Schwarz preconditioner for local \(C^0\) discontinuous Galerkin methods of Kirchhoff plates ⋮ Is There More Than One Dirichlet--Neumann Algorithm for the Biharmonic Problem? ⋮ Fourier analysis of Schwarz domain decomposition methods for the biharmonic equation

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