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Fully automatic $$hp$$-adaptivity for Maxwell’s equations. (English) Zbl 1063.78019
Summary: I report on the development of a fully automatic $$hp$$-adaptive strategy for the solution of time-harmonic Maxwell equations. The strategy produces a sequence of grids that deliver exponential convergence for both regular and singular solutions. Given a (coarse) mesh, we refine it first globally in both $$h$$ and $$p$$, and solve the problem on the resulting fine mesh. We consider then the projection-based interpolants of the fine mesh solution with respect to both current and next (to be determined) coarse grid, and introduce the interpolation error decrease rate equal to the difference of the old and new (coarse) mesh interpolation errors vs. number of degrees-of-freedom added. The optimal $$hp$$-refinements leading to the next coarse grid are then determined by maximizing the interpolation error decrease rate.

##### MSC:
 78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory 78A25 Electromagnetic theory (general) 65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
##### Keywords:
$$hp$$ edge finite elements; $$hp$$-adaptivity
2Dhp90
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##### References:
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