Abstract
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.
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Kolkovska, N.T. (2007). Numerical Solution of an Elliptic Problem with a Non-classical Boundary Condition. In: Boyanov, T., Dimova, S., Georgiev, K., Nikolov, G. (eds) Numerical Methods and Applications. NMA 2006. Lecture Notes in Computer Science, vol 4310. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70942-8_75
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DOI: https://doi.org/10.1007/978-3-540-70942-8_75
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70940-4
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