Error estimate FEM for the Nikol'skij-Lizorkin problem with degeneracy

Abstract This paper discusses the finite element approximation of the Nikol’skij–Lizorkin problem with degeneracy on the entire boundary of the domain. The triangulation of the domain with a special compression of nodes to the boundary of the domain was carried out. It was established that the approximation to the exact solution has first-order convergence in the norm of the Sobolev weighted space  W 2 , α 1 ( Ω ) at special exponent of the degree of mesh compression. Numerical experiments was confirmed the established estimate of the convergence rate.

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