Nonconforming Virtual Element Method for $2m$th Order Partial Differential Equations in $\mathbb {R}^n$

DOI10.1090/mcom/3498zbMath1436.65175arXiv1811.03295OpenAlexW2982444179MaRDI QIDQ4960073

Long Chen, Xuehai Huang

Publication date: 8 April 2020

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.03295

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) 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) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items (39)

\({H^m}\)-Conforming Virtual Elements in Arbitrary Dimension ⋮ The interior penalty virtual element method for the biharmonic problem ⋮ A C⁰ interior penalty method for mth-Laplace equation ⋮ \(C^1\)-conforming variational discretization of the biharmonic wave equation ⋮ The nonconforming virtual element method for semilinear elliptic problems ⋮ Nonconforming Virtual Elements for the Biharmonic Equation with Morley Degrees of Freedom on Polygonal Meshes ⋮ A \(C^0\)-nonconforming virtual element methods for the vibration and buckling problems of thin plates ⋮ Cut-off error splitting technique for conservative nonconforming VEM for \(N\)-coupled nonlinear Schrödinger-Boussinesq equations ⋮ The virtual element method for a nonhomogeneous double obstacle problem of Kirchhoff plate ⋮ The virtual element method with interior penalty for the fourth-order singular perturbation problem ⋮ The Hermite-type virtual element method with interior penalty for the fourth-order elliptic problem ⋮ The role of stabilization in the virtual element method: a survey ⋮ A New Locking-Free Virtual Element Method for Linear Elasticity Problems ⋮ Virtual element method for linear elastic clamped plate model ⋮ Analysis of divergence free conforming virtual elements for the Brinkman problem ⋮ The nonconforming virtual element method for Oseen’s equation using a stream-function formulation ⋮ The Morley-type virtual element method for the Navier-Stokes equations in stream-function form ⋮ Nonconforming virtual element discretization for the transmission eigenvalue problem ⋮ Virtual Element Methods Without Extrinsic Stabilization ⋮ Mixed variational formulations of virtual elements for the polyharmonic operator \((-\Delta)^n\) ⋮ Unconditional Error Analysis of VEMs for a Generalized Nonlinear Schrödinger Equation ⋮ A lowest-order locking-free nonconforming virtual element method based on the reduced integration technique for linear elasticity problems ⋮ A medius error analysis for nonconforming virtual element methods for Poisson and biharmonic equations ⋮ A posteriori error analysis of a non-consistent virtual element method for reaction diffusion equations ⋮ Conforming and nonconforming conservative virtual element methods for nonlinear Schrödinger equation: a unified framework ⋮ Enrichment of the nonconforming virtual element method with singular functions ⋮ The nonconforming virtual element method for fourth-order singular perturbation problem ⋮ The virtual element method for an obstacle problem of a Kirchhoff-Love plate ⋮ Finite Neuron Method and Convergence Analysis ⋮ The curl–curl conforming virtual element method for the quad-curl problem ⋮ The nonconforming virtual element method for the Darcy-Stokes problem ⋮ A Morley-Wang-Xu element method for a fourth order elliptic singular perturbation problem ⋮ Nonconforming virtual element method for \(2m\)th order partial differential equations in \(\mathbb{R}^n\) with \(m>n\) ⋮ Piecewise Divergence-Free Nonconforming Virtual Elements for Stokes Problem in Any Dimensions ⋮ Discrete Hessian complexes in three dimensions ⋮ The nonconforming Trefftz virtual element method: general setting, applications, and dispersion analysis for the Helmholtz equation ⋮ The conforming virtual element method for polyharmonic and elastodynamics problems: a review ⋮ 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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