6. Discretization of the problem for any domain

Let Ω be any open which, for simplicity, we will consider included in $ℝ^{2}$ . We always consider the numerical solution of the Poisson problem with homogeneous Dirichlet boundary conditions on the boundary ¶ Ω of Ω, whose formulation we recall: ${\begin{matrix} - Δ u = f dans Ω \\ u = 0 sur \partial Ω \end{matrix}$

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References

(1) - DAUTRAY (R.), LIONS (J.-L.) - Analyse mathématique et calcul numérique pour les sciences et les techniques. - Tome 1 à tome 9, Masson (1988).
(2) - FORSYTHE (G.), WASOV (W.) - Finite difference methods for partial differential equations. - Wiley...

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