A Locally Divergence-Free Interior Penalty Method for Two-Dimensional Curl-Curl Problems
A Locally Divergence-Free Interior Penalty Method for Two-Dimensional Curl-Curl Problems
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本文研究一类二维卷曲-卷曲问题的内点罚方法。该方法利用梯度网格上的局部无发散间断向量场P_1 $来计算解的无发散部分。它有最佳的顺序收敛（到任意小的$\displaystyle $）的源问题和特征值问题。数值实验结果证实了理论结果。
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.