The conforming virtual element method for polyharmonic problems
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Publication:2212313
DOI10.1016/j.camwa.2019.09.022zbMath1452.65320arXiv1811.04317OpenAlexW2979103496MaRDI QIDQ2212313
Marco Verani, Paola Francesca Antonietti, Gianmarco Manzini
Publication date: 20 November 2020
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1811.04317
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) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30)
Related Items (30)
\({H^m}\)-Conforming Virtual Elements in Arbitrary Dimension ⋮ A virtual element generalization on polygonal meshes of the Scott-Vogelius finite element method for the 2-D Stokes problem ⋮ A C0 interior penalty method for mth-Laplace equation ⋮ Stabilization of the nonconforming virtual element method ⋮ \(C^1\)-conforming variational discretization of the biharmonic wave equation ⋮ CVEM-BEM coupling with decoupled orders for 2D exterior Poisson problems ⋮ Conforming virtual element approximations of the two-dimensional Stokes problem ⋮ Polyhedral mesh quality indicator for the virtual element method ⋮ The virtual element method for a nonhomogeneous double obstacle problem of Kirchhoff plate ⋮ The virtual element method for a 2D incompressible MHD system ⋮ Virtual element method for the Sobolev equations ⋮ The role of stabilization in the virtual element method: a survey ⋮ CVEM-BEM coupling for the simulation of time-domain wave fields scattered by obstacles with complex geometries ⋮ A \(C^1\)-conforming arbitrary-order two-dimensional virtual element method for the fourth-order phase-field equation ⋮ Mixed variational formulations of virtual elements for the polyharmonic operator \((-\Delta)^n\) ⋮ Conforming VEM for general second-order elliptic problems with rough data on polygonal meshes and its application to a Poisson inverse source problem ⋮ Enrichment of the nonconforming virtual element method with singular functions ⋮ The Mixed Virtual Element Method for the Richards Equation ⋮ A virtual element method for the steady-state Poisson-Nernst-Planck equations on polygonal meshes ⋮ The virtual element method for an obstacle problem of a Kirchhoff-Love plate ⋮ Nonconforming virtual element method for \(2m\)th order partial differential equations in \(\mathbb{R}^n\) with \(m>n\) ⋮ Nonconforming Virtual Element Method for $2m$th Order Partial Differential Equations in $\mathbb {R}^n$ ⋮ Arbitrary-order intrinsic virtual element method for elliptic equations on surfaces ⋮ \(C^1 \)-VEM for some variants of the Cahn-Hilliard equation: a numerical exploration ⋮ A \(C^1\)-\(C^0\) virtual element discretization for a sixth-order elliptic equation ⋮ VEM and the mesh ⋮ The conforming virtual element method for polyharmonic and elastodynamics problems: a review ⋮ The virtual element method for the coupled system of magneto-hydrodynamics ⋮ A review on arbitrarily regular conforming virtual element methods for second- and higher-order elliptic partial differential equations ⋮ A nonconforming virtual element method for a fourth-order hemivariational inequality in Kirchhoff plate problem
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