Callihan, Robert S.; Wood, Aihua W. A modified Helmholtz equation with impedance boundary conditions. (English) Zbl 1262.65166 Adv. Appl. Math. Mech. 4, No. 6, 703-718 (2012). Summary: Here considered is the problem of transient electromagnetic scattering from overfilled cavities embedded in an impedance ground plane. An artificial boundary condition is introduced on a semicircle enclosing the cavity that couples the fields from the infinite exterior domain to those fields inside. A Green’s function solution is obtained for the exterior domain, while the interior problem is solved using finite element method. Well-posedness of the associated variational formulation is achieved and convergence and stability of the numerical scheme confirmed. Numerical experiments show the accuracy and robustness of the method. Cited in 4 Documents MSC: 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs Keywords:Helmholtz equation; impedance boundary conditions; finite element method PDFBibTeX XMLCite \textit{R. S. Callihan} and \textit{A. W. Wood}, Adv. Appl. Math. Mech. 4, No. 6, 703--718 (2012; Zbl 1262.65166) Full Text: DOI