Geodesic
Asymptotic expansions of solutions of the Helmholtz equation in the neighbourhood of boundary corner points
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 19 (1979) no. 5, pp. 1205-1216

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Complete asymptotic expansions are obtained, assuming that a piece of boundary consists of straight line segments. The Dirichlet, Neumann, and mixed boundary value problems are considered. A numerical example shows that expansions are worth using in approximate methods. 
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     author = {V. I. Dymchenko},
     title = {Asymptotic expansions of~solutions of~the {Helmholtz} equation in~the neighbourhood of~boundary corner points},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1205--1216},
     publisher = {mathdoc},
     volume = {19},
     number = {5},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1979_19_5_a11/}
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V. I. Dymchenko. Asymptotic expansions of solutions of the Helmholtz equation in the neighbourhood of boundary corner points. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 19 (1979) no. 5, pp. 1205-1216. http://geodesic.mathdoc.fr/item/ZVMMF_1979_19_5_a11/