Geodesic
Convergence of finite-difference schemes for Poisson's equation with a dynamic boundary condition
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 2, pp. 287-297

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The convergence of a finite-difference scheme applied to a two-dimensional elliptic equation with a dynamic boundary condition is analyzed. An estimate for the convergence rate is derived that is nearly compatible with the smoothness of the solution to the original boundary value problem (with an additional logarithmic factor) in a special discrete norm of the Sobolev type. 
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     author = {L. G. Volkov and B. S. Jovanovi\'c},
     title = {Convergence of finite-difference schemes for {Poisson's} equation with a dynamic boundary condition},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {287--297},
     publisher = {mathdoc},
     volume = {45},
     number = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_2_a11/}
}
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L. G. Volkov; B. S. Jovanović. Convergence of finite-difference schemes for Poisson's equation with a dynamic boundary condition. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 2, pp. 287-297. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_2_a11/