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A new error analysis of a mixed finite element method for the quad-curl problem. (English) Zbl 1428.78032

Summary: In this paper, we study a new numerical approach for a quad-curl model problem which arises in the inverse electromagnetic scattering problems and magnetohydrodynamics (MHD). We first split the quad-curl problem with homogeneous boundary conditions into a system of second order equations, and then apply a mixed finite element method to solve the resulting system. The perturbed mixed finite element method is constructed by using edge elements. The well posedness of the numerical scheme is derived. The optimal error estimates in \(H\)(curl) and \(L^2\) norms for the primal and auxiliary variables are obtained, respectively. The theoretical results are verified by numerical experiments.

MSC:

78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35Q61 Maxwell equations
65N15 Error bounds for boundary value problems involving PDEs
78M99 Basic methods for problems in optics and electromagnetic theory
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References:

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