Finite difference approximation of an elliptic problem with nonlocal boundary condition | Zendy

Sandra Hodžić | Zendy; Boško S. Jovanović | Zendy

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Finite difference approximation of an elliptic problem with nonlocal boundary condition

Author(s) -

Sandra Hodžić,

Boško S. Jovanović

Publication year - 2016

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1606549h

Subject(s) - mathematics , sobolev space , uniqueness , smoothness , mathematical analysis , norm (philosophy) , boundary value problem , poisson's equation , finite difference , unit sphere , discrete poisson equation , boundary (topology) , finite difference method , uniqueness theorem for poisson's equation , political science , law

We consider Poisson's equation on the unit square with a nonlocal boundary condition. The existence and uniqueness of its weak solution in Sobolev space $H^1$ is proved. A finite difference scheme approximating this problem is proposed. An error estimate compatible with the smoothness of input data in discrete $H^{1}$ Sobolev norm is obtained.

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