Finite element approximation of a degenerating second-order elliptic equation in a domain with curvilinear boundary (Q1842500)

This paper is concerned with the solution of a boundary value problem for linear second-order elliptic equations degenerating on the boundary of the convex domain by the finite element method (FEM). The original problem is reduced to a variational one, the existence and the uniqueness for the solution of the variational problem were established earlier. Further the approximating family of solutions of FEM schemes for the problem is constructed using special domain triangulation collection condensing near the boundary and piecewise polynomial finite elements of arbitrary degree. The convergence of FEM schemes is studied, estimates for accuracy in terms of the regular mesh size and of the condensation degree are obtained. In the last section the author gives error bounds depending on the dimension of the approximating space.