Iterative Substructuring Methods for Spectral Element Discretizations of Elliptic Systems. II: Mixed Methods for Linear Elasticity and Stokes Flow

DOI10.1137/S0036142998333092zbMath0951.65123OpenAlexW2018926979MaRDI QIDQ4943625

Publication date: 19 March 2000

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

Full work available at URL: https://doi.org/10.1137/s0036142998333092

zbMATH Keywords

linear elasticity domain decomposition preconditioning condition number spectral elements Stokes problem substructuring Krylov space method saddle point Schur complement

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Boundary value problems for second-order elliptic equations (35J25) Classical linear elasticity (74B05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Navier-Stokes equations (35Q30) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35)

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Balancing Neumann-Neumann methods for incompressible Stokes equations ⋮ Performance of parallel preconditioners for adaptive hp FEM discretization of incompressible flows ⋮ Positive definite balancing Neumann-Neumann preconditioners for nearly incompressible elasticity ⋮ Legendre spectral element method with nearly incompressible materials ⋮ A Mass Conserving Mixed $hp$-FEM Scheme for Stokes Flow. Part III: Implementation and Preconditioning ⋮ Constraint Interface Preconditioning for the Incompressible Stokes Equations ⋮ Study of a non-overlapping domain decomposition method: Poisson and Stokes problems. ⋮ BDDC and FETI-DP Preconditioners for Spectral Element Discretizations of Almost Incompressible Elasticity ⋮ Fluid-structure interaction by the spectral element method ⋮ Overlapping Schwarz and spectral element methods for linear elasticity and elastic waves ⋮ Isogeometric block FETI-DP preconditioners for the Stokes and mixed linear elasticity systems ⋮ The $hp$-mortar finite-element method for the mixed elasticity and Stokes problems ⋮ Indefinite overlapping Schwarz methods for time-dependent Stokes problems ⋮ Overlapping Schwarz Methods with a Standard Coarse Space for Almost Incompressible Linear Elasticity ⋮ A dual-primal FETI method for incompressible Stokes equations ⋮ A non-overlapping domain decomposition method for the Stokes equations via a penalty term on the interface.

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