3-dimensional potential problem; Ritz-Galerkin approximation; convergence; diffraction; nonlocal boundary condition; finite elements
Assuming an incident wave to be a field source, we calculate the field potential in a neighborhood of an inhomogeneous body. This problem which has been formulated in $\bold R^3$can be reduced to a bounded domain. Namely, a boundary condition for the potential is formulated on a sphere. Then the potential satisfies a well posed boundary value problem in a ball containing the body. A numerical approximation is suggested and its convergence is analyzed.
 V. Drápalík V. Janovský: On a potential problem with incident wave as a field source
. Aplikace matematiky 33 (1988), 443-455 MR 0973239
 J. L. Lions E. Magenes: Problèmes aux limites non homogènes et applications. Dunod, Paris 1968.
 G. C. Hsiao P. Kopp W. L. Wendland: A Galerkin collocation method for some integral equations of the first kind
. Computing 25 (1980), 89-130. DOI 10.1007/BF02259638
| MR 0620387
 C. Johnson J. C. Nedelec: On the coupling of boundary integral and finite element methods
. Math. Соmр. 35 (1980), 1063-1079. MR 0583487