Stabilization-free virtual element method for plane elasticity

2022/02/21 by Alvin Chen, N. Sukumar, Chen, Alvin +1 · 6 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2202.10037

openalex publication_date 2022/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present the construction and application of a first order stabilization-free virtual element method to problems in plane elasticity. Well-posedness and error estimates of the discrete problem are established. The method is assessed on a series of well-known benchmark problems from linear elasticity and numerical results are presented that affirm the optimal convergence rate of the virtual element method in the L² norm and the energy seminorm.

Cited by

• A coupled finite element-virtual element method for thermomechanical analysis of electronic packaging structures
• Mass-Lumped Virtual Element Method with Strong Stability-Preserving Runge-Kutta Time Stepping for Two-Dimensional Parabolic Problems
• Stabilization-free virtual element method for 2D third medium contact
• CutVEM: Conforming virtual element method on embedded domains with shape-agnostic element agglomeration
• The Neural Approximated Virtual Element Method for Elasticity Problems
• A residual a posteriori error estimate for the Stabilization-free Virtual Element Method

Related

• Stabilization-free virtual element method for 3D hyperelastic problems
• A Dual Hybrid Virtual Element Method for Plane Elasticity Problems
• A lowest-order locking-free nonconforming virtual element method based on the reduced integration technique for linear elasticity problems
• A novel locking-free virtual element method for linear elasticity problems
• High-order 3D virtual element method for linear and nonlinear elasticity