Diffusion-transport-reaction equations

Part of the MS&A book series (MS&A, volume 2)


In this chapter, we consider problems of the following form
$$ \left\{ \begin{gathered} - div(\mu \nabla u) + b \cdot \nabla u + \sigma u = f in\Omega , \hfill \\ u = 0 on\partial \Omega , \hfill \\ \end{gathered} \right. $$
where µ, σ, f and b are given functions (or constants). In the most general case, we will suppose that µ ∈ L(Ω) with µ(x) ≥ µ0 > 0, σ ∈ L2(Ω) with σ(x) ≥ 0 a.e. in Ω,b ∈ [L(Ω)]2 withdiv(b) ∈ L2(Ω), and f ∈ L2(Ω).


Bilinear Form Galerkin Method Stabilization Method Upwind Scheme Incremental Ratio 
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© Springer-Verlag Italia, Milan 2009

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