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A stabilized multidomain approach for singular perturbation problems. (English) Zbl 0757.76037
Summary: We present a new technique of stabilization for finite difference or spectral approximations of singular perturbation problems. Here we allow the artificial viscosity to be constant and independent of the step size. The results are generalized to variable coefficient problems. Suitable multigrid components are proposed. Numerical results are presented which substantiate the usefulness of our technique.

76M20Finite difference methods (fluid mechanics)
76R99Diffusion and convection (fluid mechanics)
65N12Stability and convergence of numerical methods (BVP of PDE)
65N55Multigrid methods; domain decomposition (BVP of PDE)
Full Text: DOI
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[9] Oertel, K. D., and Stüben, K. (1988). Multigrid with ILU-smoothing: systematic tests and improvements, inRobust Multigrid Methods, Notes on Numerical Fluid Mechanics, Wolfgang Hackbusch (ed.), Vol. 23, Vieweg, Braunschweig/Wiesbaden.
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[13] Thole, C. A. (1983). Beiträge zu Fourieranalyse von Mehrgittermethoden: V-cycle, ILU-Glättung, anisotrope Operatoren, Master Thesis, Bonn (unpublished).
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