Lowest-order virtual element methods for linear elasticity problems

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