Compressibility

Engineering

Linear elasticity

Applied mathematics

Convergence (economics)

Virtual work

Economics

Computer science

Mathematical optimization

Dentistry

Thermodynamics

Physics

Finite element method

Calculus (dental)

Mathematics

Elasticity (physics)

Political science

Mathematical analysis

Element (criminal law)

Structural engineering

Medicine

Economic growth

Mechanics

Computer Methods in Applied Mechanics and Engineering

We present two kinds of lowest-order virtual element methods for planar linear elasticity problems. For the first one we use the nonconforming virtual element method with a stabilizing term. It can be interpreted as a modification of the nonconforming Crouzeix–Raviart finite element method as suggested in Hansbo and Larson (2003) to the virtual element method. For the second one we use the conforming virtual element for one component of the displacement vector and the nonconforming virtual element for the other. This approach can be seen as an extension of the idea of Kouhia and Stenberg suggested in Kouhia and Stenberg (1995) to the virtual element method. We show that our proposed methods satisfy the discrete Korn’s inequality. We also prove that the methods are convergent uniformly for the nearly incompressible case and the convergence rates are optimal.

Lowest-order virtual element methods for linear elasticity problems