A modified interior penalty virtual element method for fourth-order singular perturbation problems

DOI10.1007/s10915-024-02665-4zbMATH Open1547.65176MaRDI QIDQ6608083

Fang Feng, Yue Yu

Publication date: 19 September 2024

Published in: Journal of Scientific Computing (Search for Journal in Brave)

zbMATH Keywords

perturbation parameteruniform error estimatesfourth-order singular perturbation probleminterior penalty virtual element methodmodified Morley element

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Plates (74K20) Finite element methods applied to problems in solid mechanics (74S05) 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 interpolation (65D05) Membranes (74K15) Higher-order elliptic equations (35J30) PDEs in connection with mechanics of deformable solids (35Q74)

Cites Work

• Unnamed Item
• Unnamed Item
• Equivalent projectors for 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
• On the constants in \(hp\)-finite element trace inverse inequalities.
• On the virtual element method for topology optimization on polygonal meshes: a numerical study
• The Morley-type virtual element for plate bending problems
• Some error analysis on virtual element methods
• The nonconforming virtual element method for fourth-order singular perturbation problem
• Virtual element method for simplified friction problem
• Virtual element method for semilinear sine-Gordon equation over polygonal mesh using product approximation technique
• Adaptive multi-material topology optimization with hyperelastic materials under large deformations: a virtual element approach
• A nonconforming virtual element method for a fourth-order hemivariational inequality in Kirchhoff plate problem
• The nonconforming virtual element method for a stationary Stokes hemivariational inequality with slip boundary condition
• A medius error analysis for nonconforming virtual element methods for Poisson and biharmonic equations
• The virtual element method for general elliptic hemivariational inequalities
• Virtual element method for an elliptic hemivariational inequality with applications to contact mechanics
• A nonconforming virtual element method for the Stokes problem on general meshes
• The Stokes complex for virtual elements with application to Navier-Stokes flows
• The virtual element method and its applications
• A robust nonconforming \(H^2\)-element
• On the necessity and sufficiency of the patch test for convergence of nonconforming finite elements
• The nonconforming virtual element method
• A $\mathcal{C}^0$ Interior Penalty Method for a Fourth Order Elliptic Singular Perturbation Problem
• Mimetic finite differences for elliptic problems
• Conforming Finite Element Approximations for a Fourth-Order Singular Perturbation Problem
• Poincaré--Friedrichs Inequalities for Piecewise H¹ Functions
• The fully nonconforming virtual element method for biharmonic problems
• A mixed virtual element method for the Navier–Stokes equations
• Virtual Elements for the Navier--Stokes Problem on Polygonal Meshes
• A mixed virtual element method for the pseudostress–velocity formulation of the Stokes problem
• Conforming and nonconforming virtual element methods for elliptic problems
• BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
• Nonconforming Virtual Element Method for $2m$th Order Partial Differential Equations in $\mathbb {R}^n$
• Conforming and nonconforming virtual element methods for a Kirchhoff plate contact problem
• The Hitchhiker's Guide to the Virtual Element Method
• The Mathematical Theory of Finite Element Methods
• The interior penalty virtual element method for the biharmonic problem
• The interior penalty virtual element method for the fourth-order elliptic hemivariational inequality
• The virtual element method for a 2D incompressible MHD system
• Virtual element method for a history-dependent variational-hemivariational inequality in contact problems
• The virtual element method with interior penalty for the fourth-order singular perturbation problem
• The virtual element method for the 3D resistive magnetohydrodynamic model

This page was built for publication: A modified interior penalty virtual element method for fourth-order singular perturbation problems