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Strong FEM formulation for quasi-static analysis of shielded planar transmission lines in anisotropic media

We present strong formulation of the Finite Element Method in anisotropic media for 2D closed electrostatic problems. We show that the set of strong basis functions for isotropic media must be reduced (i.e., one quadruple function omitted) in order to achieve the required C1 continuity of electrostatic potential in anisotropic media. Numerical results for characteristic impedance and effective permittivity of the shielded strip-line in three homogeneous anisotropic media (sapphire, boron-nitride, and epsilam) are given and compared with results from the literature.