The virtual element method with interior penalty for the fourth-order singular perturbation problem

DOI10.1016/j.cnsns.2024.107964OpenAlexW4392593252MaRDI QIDQ6131381

Bei Zhang, Jikun Zhao

Publication date: 5 April 2024

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2024.107964

zbMATH Keywords

singular perturbation problempolygonal meshinterior penaltyvirtual element

Mathematics Subject Classification ID

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)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(H(\mathrm{div})\) and \(H(\mathbf{curl})\)-conforming virtual element methods
• \texttt{PolyMesher}: a general-purpose mesh generator for polygonal elements written in Matlab
• Virtual element methods for plate bending problems
• Virtual element method for fourth order problems: \(L^2\)-estimates
• \(C^0\) interior penalty methods for fourth order elliptic boundary value problems on polygonal domains
• A family of non-conforming elements and the analysis of Nitsche's method for a singularly perturbed fourth order problem
• Non-conforming harmonic virtual element method: \(h\)- and \(p\)-versions
• The Morley-type virtual element for plate bending problems
• Morley-Wang-Xu element methods with penalty for a fourth order elliptic singular perturbation problem
• The nonconforming virtual element method for fourth-order singular perturbation problem
• A \(C^1\) virtual element method on polyhedral meshes
• A medius error analysis for nonconforming virtual element methods for Poisson and biharmonic equations
• A robust nonconforming $H^2$-element
• The nonconforming virtual element method
• The nonconforming virtual element method for plate bending problems
• Divergence free virtual elements for the stokes problem on polygonal meshes
• A $\mathcal{C}^0$ Interior Penalty Method for a Fourth Order Elliptic Singular Perturbation Problem
• 𝒞⁰ penalty methods for the fully nonlinear Monge-Ampère equation
• Virtual element methods on meshes with small edges or faces
• Stability analysis for the virtual element method
• The fully nonconforming virtual element method for biharmonic problems
• BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
• Uniformly stable rectangular elements for fourth order elliptic singular perturbation problems
• Nonconforming Virtual Element Method for $2m$th Order Partial Differential Equations in $\mathbb {R}^n$
• The curl–curl conforming virtual element method for the quad-curl problem
• The Divergence-Free Nonconforming Virtual Element for the Stokes Problem
• A virtual element method for the Steklov eigenvalue problem
• Uniformly Convergent Nonconforming Element for 3-D Fourth Order Elliptic Singular Perturbation Problem
• \({H^m}\)-Conforming Virtual Elements in Arbitrary Dimension
• The interior penalty virtual element method for the biharmonic problem
• The role of stabilization in the virtual element method: a survey

This page was built for publication: The virtual element method with interior penalty for the fourth-order singular perturbation problem