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An arbitrary high-order spline finite element solver for the time domain Maxwell equations. (English) Zbl 1247.78042

Higher-order methods for solving time-domain Maxwell equations using spline finite elements are applied. After recalling the variational formulation of 2D Maxwell equations, the authors construct an exact sequence of discrete spaces as spans of basis functions on a Cartesian grid. A central result of the paper under review establishes a stability condition when a leap-Frog algorithm in time is used. Higher-order convergence is also obtained, and the CFL conditions are computed for different degrees of splines.

MSC:

78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
78M30 Variational methods applied to problems in optics and electromagnetic theory
65D07 Numerical computation using splines
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