Geodesic
Finite element method for the diffraction problem in a waveguide
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 11, pp. 1926-1930

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The convergence of the finite element method (FEM) as applied to the diffraction problem in a waveguide in the case when there is no damping in the medium filling the waveguide is proved. A functional space that takes into account the partial radiation conditions is introduced to carry out the proof. A highly accurate approximation method for the partial radiation conditions is considered. 
@article{ZVMMF_2010_50_11_a5,
     author = {A. L. Delitsyn},
     title = {Finite element method for the diffraction problem in a waveguide},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1926--1930},
     publisher = {mathdoc},
     volume = {50},
     number = {11},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_11_a5/}
}
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A. L. Delitsyn. Finite element method for the diffraction problem in a waveguide. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 11, pp. 1926-1930. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_11_a5/