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CCT-TR-2008-3
Title:
A Nonconforming Penalty Method For A Two Dimensional Curl-Curl Problem
Authors:
Susanne C. Brenner, Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, LA 70803
Li-yeng Sung, Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803
Summary:
A nonconforming penalty method for a two-dimensional curl-curl problem is studied in this paper. It uses weakly continuous P1 vector fields and penalizes the local divergence. Two consistency terms involving the jumps of the vector fields across element boundaries are also included to ensure the convergence of the scheme. Optimal convergence rates (up to an arbitrary positive ε) in both the energy norm and the L2 norm are established on graded meshes. This scheme can also be used in the computation of Maxwell eigenvalues without generating spurious eigenmodes. The theoretical results are con?rmed by numerical experiments.
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CCT-TR-2008-3.pdf
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