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Abstract
We first propose and analyze two variational formulations of the curl-div system that rewrite it as a saddle-point problem. Existence and uniqueness results are then an easy consequence of this approach. Second, introducing suitable constrained Hilbert spaces, we devise other variational formulations that turn out to be useful for numerical approximation. Curl-free and divergence-free finite elements are employed for discretizing the problem, and the corresponding finite element solutions are shown to converge to the exact solution. Several numerical tests are also included, illustrating the performance of the proposed approximation methods.