A multigrid algorithm for the p-version of the virtual element method

DOI10.1051/m2an/2018007zbMath1397.65249arXiv1703.02285OpenAlexW2963440819MaRDI QIDQ4579928

Marco Verani, Paola Francesca Antonietti

Publication date: 10 August 2018

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.02285

zbMATH Keywords

Poisson problemiterative solvervirtual element methodpolygonal mesh\(p\)-multigrid\(p\)-Galerkin method

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) 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 (24)

Agglomeration-Based Geometric Multigrid Schemes for the Virtual Element Method ⋮ Non-conforming harmonic virtual element method: \(h\)- and \(p\)-versions ⋮ Stabilization of the nonconforming virtual element method ⋮ BDDC preconditioners for divergence free virtual element discretizations of the Stokes equations ⋮ Robust and scalable adaptive BDDC preconditioners for virtual element discretizations of elliptic partial differential equations in mixed form ⋮ The role of stabilization in the virtual element method: a survey ⋮ Reduced basis stabilization and post-processing for the virtual element method ⋮ Parallel block preconditioners for virtual element discretizations of the time-dependent Maxwell equations ⋮ FETI-DP for the Three Dimensional Virtual Element Method ⋮ BDDC Preconditioners for Virtual Element Approximations of the Three-Dimensional Stokes Equations ⋮ A fully discrete virtual element scheme for the Cahn-Hilliard equation in mixed form ⋮ Parallel solvers for virtual element discretizations of elliptic equations in mixed form ⋮ The conforming virtual element method for polyharmonic problems ⋮ Ill‐conditioning in the virtual element method: Stabilizations and bases ⋮ A numerical study of the virtual element method in anisotropic diffusion problems ⋮ Parallel block preconditioners for three-dimensional virtual element discretizations of saddle-point problems ⋮ The Virtual Element Method with curved edges ⋮ A posteriori error estimation and adaptivity in \textit{hp} virtual elements ⋮ High order VEM on curved domains ⋮ Adaptive virtual element methods with equilibrated fluxes ⋮ An improved multigrid solver for the \(p\)-hierarchical basis finite element method using a space decomposition smoother ⋮ Weakly imposed Dirichlet boundary conditions for 2D and 3D virtual elements ⋮ VEM and the mesh ⋮ A review on arbitrarily regular conforming virtual element methods for second- and higher-order elliptic partial differential equations

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