Agglomeration-Based Geometric Multigrid Schemes for the Virtual Element Method

DOI10.1137/21M1466864MaRDI QIDQ5886231

Martina Busetto, Stefano Berrone, Marco Verani, Paola Francesca Antonietti

Publication date: 31 March 2023

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

Full work available at URL: https://arxiv.org/abs/2112.11080

zbMATH Keywords

elliptic problemsagglomerationvirtual element methodpolygonal meshesgeometric multigrid algorithms

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) 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) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items

Reduced basis stabilization and post-processing for the virtual element method ⋮ BDDC Preconditioners for Virtual Element Approximations of the Three-Dimensional Stokes Equations

Uses Software

• Triangle

Cites Work

• Equivalent projectors for virtual element methods
• Multigrid algorithms for \(hp\)-version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes
• BDDC and FETI-DP for the virtual element method
• \(V\)-cycle multigrid algorithms for discontinuous Galerkin methods on non-nested polytopic meshes
• Some error analysis on virtual element methods
• FETI-DP preconditioners for the virtual element method on general 2D meshes
• Parallel block preconditioners for three-dimensional virtual element discretizations of saddle-point problems
• An overlapping Schwarz method for virtual element discretizations in two dimensions
• The virtual element method and its applications
• Virtual Element Method for general second-order elliptic problems on polygonal meshes
• A generalized BPX multigrid framework covering nonnested V-cycle methods
• New Convergence Estimates for Multigrid Algorithms
• The Analysis of Smoothers for Multigrid Algorithms
• Convergence of nonconforming multigrid methods without full elliptic regularity
• On the approximation of a virtual coarse space for domain decomposition methods in two dimensions
• A multigrid algorithm for the p-version of the virtual element method
• Ill‐conditioning in the virtual element method: Stabilizations and bases
• BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
• Recent results and perspectives for virtual element methods
• The Analysis of Multigrid Algorithms with Nonnested Spaces or Noninherited Quadratic Forms

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