A Locally Divergence-Free Interior Penalty Method for Two-Dimensional Curl-Curl Problems

Authors:
Susanne C. Brenner;Fengyan Li;Li-Yeng Sung
Affiliations:
-;-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2008

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Abstract

An interior penalty method for certain two-dimensional curl-curl problems is investigated in this paper. This method computes the divergence-free part of the solution using locally divergence-free discontinuous $P_1$ vector fields on graded meshes. It has optimal order convergence (up to an arbitrarily small $\epsilon$) for the source problem and the eigenproblem. Results of numerical experiments that corroborate the theoretical results are also presented.