2. Spectral discretization of an elliptic equation
We'll start by describing spectral discretization in the case of a model problem: the Laplace equation with homogeneous Dirichlet boundary conditions. We'll then look at how to deal with more complex boundary conditions. Finally, we will allude to the various equations in mechanics and physics that have been discretized by spectral methods, and give references for more detailed results.
2.1 Discretization of a Laplace equation
We first consider the basic equation in the square or cube Ω
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Spectral discretization of an elliptic equation
Handling complex geometries
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Bibliography
- (1) - ABRAMOWITZ (M.), STEGUN (I.A.) - Handbook of mathematical functions with formulas, graphs, and mathematical tables, vol. 55 of National Bureau of Standards Applied Mathematics Series - For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. (1964).
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