Abstract
Darwin model is a good approximation to Maxwell's equations, and this paper is concerned with the boundary value problem of the Darwin model in three-dimensional exterior domains. Firstly we establish the variational formulations of Darwin model in exterior domains and prove the existence and uniqueness. Then we prove a useful decomposition theorem that any function in unbounded exterior domains belonging to L2(Ω) can be decomposed into the sum of a function's gradient and another function's rotation, such decomposition is crucial in inducing the Darwin model. At last we spend some energy in using the infinite element method to solve the Darwin model in axis-symmetric exterior domains cases. Error estimates are obtained in weighted spaces, and numerical examples verify the convergence once again.
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