MIXED FINITE VOLUME METHOD FOR TWO-DIMENSIONAL MAXWELL'S EQUATIONS

초록

We propose and analyze a mixed finite volume method for the two-dimensional time-harmonic Maxwell's equations which simultaneously approximates the vector field u and the scalar function xi = mu(-1 )curl u. The method chooses the lowest-order Nedelec edge element for u and the P1 Crouzeix-Raviart nonconforming element for xi on triangular meshes. It is shown that the method is reduced to a modified P1 nonconforming FEM for xi or a modified edge element method for u by eliminating the discrete variable of u or xi . After solving the reduced method, the eliminated discrete variable can be recovered from the other one via a simple local formula. Using this feature, we also derive optimal a priori error estimates under weak regularity assumptions and show that the approximation to xi has a higher-order of convergence in the L-2 norm than the one obtained by direct differentiation of the approximation to uu when the exact solution is sufficiently smooth.

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