2007 | OriginalPaper | Buchkapitel
Numerical Solution of an Elliptic Problem with a Non-classical Boundary Condition
verfasst von : Natalia T. Kolkovska
Erschienen in: Numerical Methods and Applications
Verlag: Springer Berlin Heidelberg
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We investigate an elliptic problem with a boundary condition given by a sum of normal derivative and an elliptic operator in tangential variables (also known as ”Venttsel” boundary condition). The differential problem is discretized by a specific finite difference method. Error estimates of the numerical method in the discrete Sobolev space
$W_2 ^1$
are obtained. The rate of convergence in this space is optimal, i.e. it is
m
− 1 for solutions from
$W_2 ^{m}$
, 1 <
m
< 2.5.