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 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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