Mixed finite element approximation of a degenerate elliptic problem
The authors continue their thorough study of a degenerate elliptic problem that arises in the study of the electromagnetic field in a structure with cylindrical symmetry. In their previous work a conforming finite element discretization had been used to deal numerically with a weak formulation of the problem; here a mixed finite element approach is proposed for a mixed formulation in appropriate weighted (Sobolev) spaces; the weight takes into account the singularity in the problem. The existence of a unique solution for the mixed formulation is first proven; then the second part of the paper introduces convenient finite element spaces for which appropriate interpolants are defined; finally and most importantly, optimal error bounds are obtained for the finite element approximations.
scientific article; zbMATH DE number 802462