, Volume 109, Issue 4, pp 509-533
Date: 26 Apr 2008

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

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Abstract

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 \({\epsilon}\)) in both the energy norm and the L 2 norm are established on graded meshes. The theoretical results are confirmed by numerical experiments.