Investigation of a preconditioner for the \(P_{2} - P_{1}\) finite element solution of Stokes problem

DOI10.1016/j.amc.2006.08.002zbMath1114.65138OpenAlexW2063794360MaRDI QIDQ876620

M. Bagheroskoui, Mohammed Hosseini Ali Abadi

Publication date: 26 April 2007

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2006.08.002

zbMATH Keywords

numerical examplespreconditioningcondition numberpenalty methodconjugate residual method\(P_{2}- P_{1}\) finite element methodindefinite stiffness matrix

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Stokes and related (Oseen, etc.) flows (76D07) 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) Finite element methods applied to problems in fluid mechanics (76M10)

Cites Work

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• Necessary and sufficient conditions for the simplification of generalized conjugate-gradient algorithms
• An analysis of a mixed finite element method for the Navier-Stokes equations
• A Taxonomy for Conjugate Gradient Methods
• Numerical solution of saddle point problems
• A Preconditioning Technique for Indefinite Systems Resulting from Mixed Approximations of Elliptic Problems
• Mixed and Hybrid Finite Element Methods
• An Optimal Preconditioner for a Class of Saddle Point Problems with a Penalty Term
• A Posteriori Error Estimation for Stabilized Mixed Approximations of the Stokes Equations
• Equivalent Norms for Sobolev Spaces

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