Hodge decomposition for divergence-free vector fields and two-dimensional Maxwell’s equations

Brenner, S.; Cui, J.; Nan, Z.; Sung, L.-Y.

doi:10.1090/S0025-5718-2011-02540-8

Hodge decomposition for divergence-free vector fields and two-dimensional Maxwell’s equations
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by S. C. Brenner, J. Cui, Z. Nan and L.-Y. Sung PDF

Math. Comp. 81 (2012), 643-659 Request permission

Abstract:

We propose a new numerical approach for two-dimensional Maxwell’s equations that is based on the Hodge decomposition for divergence-free vector fields. In this approach an approximate solution for Maxwell’s equations can be obtained by solving standard second order scalar elliptic boundary value problems. This new approach is illustrated by a $P_1$ finite element method.

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