Mesh orientation and anisotropic refinement in the streamline diffusion method. (English) Zbl 0812.76047

Zhou, Guohui; Rannacher, Rolf

Křižek, M. (ed.) et al., Finite element methods. 50 years of the Courant element. Conference held at the Univ. of Jyväskylä, Finland, 1993. New York, NY: Marcel Dekker, Inc. Lect. Notes Pure Appl. Math. 164, 491-500 (1994).

Summary: The effect of mesh orientation is analysed for the streamline diffusion finite element for scalar convection-dominated convection-diffusion problems. By orienting and stretching the elements in the streamline direction, the order of pointwise convergence can be increased from \(O(h^{11/8})\) to \(O(h^{15/8})\), which improves earlier results by half an order. This suggests the use of anisotropic mesh refinement along the “interior layers” in order to obtain an accurate approximation for nonsmooth inflow data.
For the entire collection see [Zbl 0802.00026].

MSC:

76M10	Finite element methods applied to problems in fluid mechanics
76R99	Diffusion and convection

Keywords:

convection-dominated convection-diffusion problems; convergence; nonsmooth inflow data