Geodesic
A rigorous justification and estimation of the rate of convergence for the partial domain method in two-dimensional eigenvalue problems for the Laplace operator
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 7, pp. 1057-1070

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The partial domain method for problems of the type indicated in the title of this paper is treated as a version either of Weinstein's method of intermediate problems or of the Ritz method. This yields a rigorous justification of the method and enables one to estimate its rate of convergence. The justification technique is demonstrated in detail for the problem of the normal modes of an $\mathrm L$-shaped membrane clamped at its edges. 
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     author = {L. T. Poznyak},
     title = {A~rigorous justification and estimation of the rate of convergence for the partial domain method in two-dimensional eigenvalue problems for the {Laplace} operator},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1057--1070},
     publisher = {mathdoc},
     volume = {30},
     number = {7},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_7_a7/}
}
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L. T. Poznyak. A rigorous justification and estimation of the rate of convergence for the partial domain method in two-dimensional eigenvalue problems for the Laplace operator. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 7, pp. 1057-1070. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_7_a7/