On the Error Estimation of the FEM for the Nikol’skij-Lizorkin Problem with Degeneracy in the Lebesgue Space

Abstract

In this manuscript, the Nikol’skii-Lizorkin problem with degeneracy on the entire boundary of the domain is considered. The degeneracy is caused by the behavior of the coefficients and right-hand sides of the problem on the boundary. The triangulation of the domain with a special compression to the boundary of the domain is carried out and the finite element method is constructed. An estimate for the rate of convergence of an approximate solution to an exact solution with the second order in the mesh step in the L2(Ω) space norm is proved. Numerical experiments have confirmed the established estimate of the convergence rate.

Keywords

• Nikol’skij–Lizorkin problem with degeneracy
• finite element method
• error estimate
• numerical experiments