In this chapter, the two-dimensional elasticity problem with a singularity caused by the presence of a re-entrant corner on the domain boundary is considered. For this problem, the notion of the Rv-generalized solution is introduced. On the basis of the Rv-generalized solution, a scheme of the weighted finite-element method (FEM) is constructed. The proposed method provides a first-order convergence of the approximate solution to the exact one with respect to the mesh step in the W 2 , ν 1 Ω -norm. The convergence rate does not depend on the size of the angle and kind of the boundary conditions imposed on its sides. Comparative analysis of the proposed method with a classical finite-element method and with an FEM with geometric mesh refinement to the singular point is carried out.
Part of the book: Finite Element Method