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 W2,α1(Ω) at special exponent of the degree of mesh compression. Numerical experiments confirmed the established estimate of the convergence rate.
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