Finite-difference method for stationary PDEs : Discretization of the problem. Square and cubic domains

Discretization of the problem. Square and cubic domains
Finite-difference method for stationary PDEs

Author : Pierre SPITERI

Publication date: October 10, 2002 | Lire en français

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3. Discretization of the problem. Square and cubic domains

Let $Ω = [0, 1] \times [0, 1]$ now correspond to the unit square. We wish to discretize the Poisson problem with homogeneous Dirichlet boundary conditions in this domain Ω, i.e. : ${\begin{matrix} - Δ u = f & dans Ω \\ u = 0 & sur \end{matrix}$

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Discretization of the problem. Square and cubic domains

(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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