International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 2, Pages 311-350
doi:10.1155/S0161171280000233
A finite element method for exterior interface problems
Richard C. MacCamy1
and S.P. Marin2
1Department of Mathematics, Carnegie-Mellon University, Pittsburgh 15213, Pennsylvania, USA
2Department of Mathematics, General Motors Research Laboratories, Warren 48090, Michigan, USA
Abstract
A procedure is given for the approximate solution of a class of two-dimensional diffraction problems. Here the usual inner boundary conditions are replaced by an inner region together with interface conditions. The interface problem is treated by a variational procedure into which the infinite region behavior is incorporated by the use of a non-local boundary condition over an auxiliary curve. The variational problem is formulated and existence of a solution established. Then a corresponding approximate variational problem is given and optimal convergence results established. Numerical results are presented which confirm the convergence rates.