Weighted FEM for Two-Dimensional Elasticity Problem with Corner Singularity

In this paper we consider homogeneous Dirichlet problem for the Lame system with singularity caused by the reentrant corner to the boundary of the two-dimensional domain. For this problem we define the solution as a R ν -generalized one; we state its existence and uniqueness in the weighted set \(\mathring{\mathbf{W}}_{2,\nu }^{1}(\varOmega,\delta )\). On the basis of the R ν -generalized solution we construct weighted finite element method. We prove that the approximate solution converges to the exact one with the rate O(h) in the norm of W2, ν1(Ω), and results of numerical experiments are presented.