Abstract
We consider the Lamé system posed in a domain with the reentrant corner of 2π as a mathematical model for the crack problem. We construct a version of the weighted finite-element method (FEM) on the base of a novel definition of the Rν-generalized solution. This allows us to suppress the influence of the singularity caused by the presence of the reentrant corner on the accuracy of computation of the approximate solution. Comparative numerical analysis of the presented approach with classical FEM and the method with mesh refinement has shown its advantages in the computational accuracy and stability as well as in the use of high-dimensional meshes. The results of investigation of the accuracy of solution to the model problem are presented in the Sobolev and energy norms. An absolute error in the mesh nodes is also analyzed.
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