Nonconforming virtual element method for \(2m\)th order partial differential equations in \(\mathbb{R}^n\) with \(m>n\)

DOI10.1007/s10092-020-00381-7zbMath1468.65192arXiv1910.12485OpenAlexW3104024956WikidataQ115385376 ScholiaQ115385376MaRDI QIDQ2033530

Xuehai Huang

Publication date: 17 June 2021

Published in: Calcolo (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.12485

zbMATH Keywords

error analysispolyharmonic equationnorm equivalence\(H^m\)-nonconforming virtual elementgeneralized Green's identity

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

\({H^m}\)-Conforming Virtual Elements in Arbitrary Dimension, A C⁰ interior penalty method for mth-Laplace equation, A posteriori error estimation for a \(C^1\) virtual element method of Kirchhoff plates, A New Locking-Free Virtual Element Method for Linear Elasticity Problems, Analysis of divergence free conforming virtual elements for the Brinkman problem, Virtual Element Methods Without Extrinsic Stabilization, Mixed variational formulations of virtual elements for the polyharmonic operator \((-\Delta)^n\), A lowest-order locking-free nonconforming virtual element method based on the reduced integration technique for linear elasticity problems, Piecewise Divergence-Free Nonconforming Virtual Elements for Stokes Problem in Any Dimensions, Discrete Hessian complexes in three dimensions, A review on arbitrarily regular conforming virtual element methods for second- and higher-order elliptic partial differential equations

Cites Work

• Unnamed Item
• Unnamed Item
• Virtual element methods for plate bending problems
• On the choice of the internal degrees of freedom for the nodal virtual element method in two dimensions
• A family of 3D continuously differentiable finite elements on tetrahedral grids
• Serendipity nodal VEM spaces
• The Morley-type virtual element for plate bending problems
• Some error analysis on virtual element methods
• Serendipity virtual elements for general elliptic equations in three dimensions
• A \(C^1\) virtual element method on polyhedral meshes
• The conforming virtual element method for polyharmonic problems
• A cubic \(H^3\)-nonconforming finite element
• The Morley element for fourth order elliptic equations in any dimensions
• Interpolation polynomials on the triangle
• The nonconforming virtual element method
• The nonconforming virtual element method for plate bending problems
• Virtual Element Implementation for General Elliptic Equations
• An interior penalty method for a sixth-order elliptic equation
• The Lowest Order Differentiable Finite Element on Rectangular Grids
• Nonconforming finite element spaces for $2m$th order partial differential equations on $\mathbb {R}^n$ simplicial grids when $m=n+1$
• Virtual element methods on meshes with small edges or faces
• The fully nonconforming virtual element method for biharmonic problems
• A nonconforming Crouzeix-Raviart type finite element on polygonal meshes
• BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
• Minimal finite element spaces for $2m$-th-order partial differential equations in $R^n$
• On the Full C₁-Q_k Finite Element Spaces on Rectangles and Cuboids
• Nonconforming Virtual Element Method for $2m$th Order Partial Differential Equations in $\mathbb {R}^n$
• A mixed finite element method for a sixth-order elliptic problem
• The Hitchhiker's Guide to the Virtual Element Method
• Stable splitting of polyharmonic operators by generalized Stokes systems
• A virtual element method with arbitrary regularity
• The Mathematical Theory of Finite Element Methods
• The minimal conforming $H^k$ finite element spaces on $R^n$ rectangular grids
• Triangular Elements in the Finite Element Method
• A New Discretization for $m$th-Laplace Equations with Arbitrary Polynomial Degrees