On the Characterization of Asymptotic Cases of the Diffusion Equation with Rough Coefficients and Applications to Preconditioning
Burak Aksoylu, Horst R. Beyer · Numerical Functional Analysis and Optimization · 2009
We consider the diffusion equation in the setting of operator theory. In particular, we study the characterization of the limit of the diffusion operator for diffusivities approaching zero on a subdomain Ω1 of the domain of integration of Ω. We generalize Lion' results to covering the case of diffusivities that are piecewise C 1 up to the boundary of Ω1 and Ω2, where instead of piecewise constant coefficients. In addition, we extend both Lion' and our previous results by providing the strong convergence of , for a monotonically decreasing sequence of diffusivities ()ν∈ℕ*.