International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 2, Pages 311-350
A finite element method for exterior interface problems
1Department of Mathematics, Carnegie-Mellon University, Pittsburgh 15213, Pennsylvania, USA
2Department of Mathematics, General Motors Research Laboratories, Warren 48090, Michigan, USA
Received 10 January 1979
Copyright © 1980 R. C. Maccamy and S. P. Marin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.