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Modeling of electromagnetic absorption/scattering problems using $$hp$$-adaptive finite elements. (English) Zbl 0994.78011
Using a variational formulation and Lagrange multipliers the authors study steady-state Maxwell equations leading to $$hp$$-adaptive finite element methods. They prove stability, uniqueness, existence and convergence of the new methods.

##### MSC:
 78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory 78A45 Diffraction, scattering 65N22 Numerical solution of discretized equations for boundary value problems involving PDEs 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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