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Article

Vejchodský, Tomáš ; Šolín, Pavel
Discrete Green's function and maximum principles. (English). In: Chleboun, J., Segeth, K. and Vejchodský, T. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Prague, May 28-31, 2006. Institute of Mathematics AS CR, Prague, 2006. pp. 247-252
Summary:
In this paper the discrete Green's function (DGF) is introduced and its fundamental properties are proven. Further it is indicated how to use these results to prove the discrete maximum principle for 1D Poisson equation discretized by the $hp$-FEM with pure Dirichlet or with mixed Dirichlet-Neumann boundary conditions and with piecewise constant coefficient.
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