CBS constants for multilevel splitting of graph-Laplacian and application to preconditioning of discontinuous Galerkin systems

DOI10.1016/j.jco.2006.10.003zbMath1145.65098OpenAlexW1975712376MaRDI QIDQ2465284

Raytcho D. Lazarov, Svetozar Margenov

Publication date: 9 January 2008

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jco.2006.10.003

zbMATH Keywords

complexitydiscontinuous Galerkin methodsecond-order elliptic equationinterior penaltygraph-Laplacianmultilevel preconditioningCauchy-Bunyakowski-Schwarz (CBS) inequality

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) Numerical computation of matrix norms, conditioning, scaling (65F35) Complexity and performance of numerical algorithms (65Y20)

Related Items (5)

Algebraic multigrid for finite element elasticity equations: Determination of nodal dependence via edge-matrices and two-level convergence ⋮ Neumann-Neumann methods for a DG discretization on geometrically nonconforming substructures ⋮ On the robustness and optimality of algebraic multilevel methods for reaction-diffusion type problems ⋮ A deluxe FETI-DP preconditioner for a composite finite element and DG method ⋮ Multilevel Splitting of Weighted Graph-Laplacian Arising in Non-conforming Mixed FEM Elliptic Problems

Cites Work

• A multilevel discontinuous Galerkin method
• The analysis of multigrid algorithms for cell centered finite difference methods
• Algebraic Multilevel Preconditioning Methods, II
• On two‐grid convergence estimates
• Robust optimal multilevel preconditioners for non‐conforming finite element systems
• Two‐level preconditioning of discontinuous Galerkin approximations of second‐order elliptic equations
• The Role of the Strengthened Cauchy–Buniakowskii–Schwarz Inequality in Multilevel Methods
• Hybrid V-Cycle Algebraic Multilevel Preconditioners
• Iterative Solution Methods
• Discontinuous Galerkin methods
• A Priori Error Estimates for Finite Element Methods Based on Discontinuous Approximation Spaces for Elliptic Problems
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• Convergence of Multigrid Algorithms for Interior Penalty Methods
• A stabilized discontinuous finite element method for elliptic problems
• Uniform estimate of the constant in the strengthened CBS inequality for anisotropic non‐conforming FEM systems

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