Multigrid method and multilevel additive preconditioner for mixed element method for non-self-adjoint and indefinite problems

DOI10.1016/S0096-3003(99)00273-8zbMath1023.65128MaRDI QIDQ1854957

Jinru Chen

Publication date: 28 January 2003

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

zbMATH Keywords

convergencepreconditionerGMRES methodmixed finite element\(V\)-cycle multigrid methodindefinite second-order elliptic 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) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Orthogonalization in numerical linear algebra (65F25)

Cites Work

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• Preconditioning projection nonconforming element method for the lowest-order Raviart-Thomas mixed triangular element method
• Schwarz alternating and iterative refinement methods for mixed formulations of elliptic problems. I: Algorithms and numerical results
• Schwarz alternating and iterative refinement methods for mixed formulations of elliptic problems. II: Convergence theory
• Uniform convergence and preconditioning methods for projection nonconforming and mixed methods for nonselfadjoint and indefinite problems
• Convergence and domain decomposition algorithm for nonconforming and mixed methods for nonselfadjoint and indefinite problems
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• A Multigrid Algorithm for the Lowest-Order Raviart–Thomas Mixed Triangular Finite Element Method
• Preconditioning Nonconforming Finite Element Methods
• Uniform Convergence of Multigrid V-Cycle Iterations for Indefinite and Nonsymmetric Problems
• Multigrid Algorithms for Nonconforming and Mixed Methods for Nonsymmetric and Indefinite Problems
• On the Implementation of Mixed Methods as Nonconforming Methods for Second- Order Elliptic Problems
• Some new error estimates for Ritz–Galerkin methods with minimal regularity assumptions
• Domain decomposition algorithms for mixed methods for second-order elliptic problems
• New Estimates for Multilevel Algorithms Including the V-Cycle