Geodesic
A hybrid method for numerical solution of Poisson’s equation in a domain with a dielectric corner
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 8, pp. 1321-1330

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An electrostatic problem of determining a potential in a domain containing an incoming dielectric corner, which reduces to solving Poisson’s equation in this domain, is considered. A specific feature of the solution of this problem is that it is bounded in a neighborhood of the dielectric corner but its gradient increases without limit. An efficient hybrid algorithm for the numerical solution of the problem, based on the finite element method and taking into account the known asymptotic representation of the solution in the neighborhood of the dielectric corner, is proposed. 
@article{ZVMMF_2017_57_8_a7,
     author = {A. N. Bogolyubov and A. I. Erokhin and I. E. Mogilevskii and M. Svetkin},
     title = {A hybrid method for numerical solution of {Poisson{\textquoteright}s} equation in a domain with a dielectric corner},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1321--1330},
     publisher = {mathdoc},
     volume = {57},
     number = {8},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_8_a7/}
}
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A. N. Bogolyubov; A. I. Erokhin; I. E. Mogilevskii; M. Svetkin. A hybrid method for numerical solution of Poisson’s equation in a domain with a dielectric corner. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 8, pp. 1321-1330. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_8_a7/