A nonconforming finite element method for a two-dimensional curl-curl and grad-div problem

摘要

A numerical method for a two-dimensional curl-curl and grad-div problem is studied in this paper. It is based on a discretization using weakly continuous P-1 vector fields and includes two consistency terms involving the jumps of the vector fields across element boundaries. Optimal convergence rates ( up to an arbitrary positive is an element of) in both the energy norm and the L-2 norm are established on graded meshes. The theoretical results are confirmed by numerical experiments.