On the multilevel preconditioning of Crouzeix–Raviart elliptic problems

DOI10.1002/nla.543zbMath1212.65491OpenAlexW2051483608MaRDI QIDQ3588918

J. Synka, Svetozar Margenov, Johannes Kraus

Publication date: 10 September 2010

Published in: Numerical Linear Algebra with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/nla.543

zbMATH Keywords

numerical resultsanisotropynon-conforming finite elementsCauchy-Bunyakowski-Schwarz inequalitymultilevel preconditioningCrouzeix-Raviart type elementsfirst reduce methodhierarchical splittingsmethod based on differences and aggregates

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) 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) Preconditioners for iterative methods (65F08)

Related Items (12)

Analysis of a two-level method for anisotropic diffusion equations on aligned and nonaligned grids ⋮ Uniformly convergent iterative methods for discontinuous Galerkin discretizations ⋮ A multilevel preconditioner for the C-R FEM for elliptic problems with discontinuous coefficients ⋮ Robust Balanced Semi-coarsening Multilevel Preconditioning of Bicubic FEM Systems ⋮ Robust semi-coarsening multilevel preconditioning of biquadratic FEM systems ⋮ Robust AMLI methods for parabolic Crouzeix-Raviart FEM systems ⋮ Multilevel algorithms for Rannacher-Turek finite element approximation of 3D elliptic problems ⋮ Preconditioning Heterogeneous $\boldsymbol{H}(\mathrm{div})$ Problems by Additive Schur Complement Approximation and Applications ⋮ BPX Preconditioner for Nonstandard Finite Element Methods for Diffusion Problems ⋮ Application of Hierarchical Decomposition: Preconditioners and Error Estimates for Conforming and Nonconforming FEM ⋮ The Effect of a Minimum Angle Condition on the Preconditioning of the Pivot Block Arising from 2-Level-Splittings of Crouzeix-Raviart FE-Spaces ⋮ Algebraic multilevel iteration method for lowest order Raviart-Thomas space and applications

Cites Work

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• Multilevel Preconditioning of 2D Rannacher-Turek FE Problems; Additive and Multiplicative Methods

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