On spurious oscillations at layers diminishing (SOLD) methods for convection–diffusion equations: Part II – Analysis for P₁ and Q₁ finite elements

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• 作者：Volker John ; Petr Knobloch
• 关键词：Convection&#x2013 ; diffusion equations ; Streamline upwind/Petrov&#x2013 ; Galerkin (SUPG) method ; Spurious oscillations at layers diminishing (SOLD) methods
• 刊名：Computer Methods in Applied Mechanics and Engineering
• 出版年：2008
• 期刊代码：27_00457825
• 类别：cp
• 出版时间：1 April 2008
• 卷：197
• 期：21-24
• 页码：1997-2014
• 文件大小：727 K

摘要

An unwelcome feature of the popular streamline upwind/Petrov–Galerkin (SUPG) stabilization of convection-dominated convection–diffusion equations is the presence of spurious oscillations at layers. A review and a comparison of the most methods which have been proposed to remove or, at least, to diminish these oscillations without leading to excessive smearing of the layers are given in Part I, [V. John, P. Knobloch, On spurious oscillations at layers diminishing (SOLD) methods for convection–diffusion equations: Part I – A review, Comput. Methods Appl. Mech. Engrg. 196 (2007) 2197–2215]. In the present paper, the most promising of these SOLD methods are investigated in more detail for P₁ and Q₁ finite elements. In particular, the dependence of the results on the mesh, the data of the problems and parameters of the methods are studied analytically and numerically. Furthermore, the numerical solution of the nonlinear discrete problems is discussed and the capability of adaptively refined grids for reducing spurious oscillations is examined. Our conclusion is that, also for simple problems, any of the SOLD methods generally provides solutions with non-negligible spurious oscillations.