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February  2009, 23(1&2): 315-339. doi: 10.3934/dcds.2009.23.315

Interaction of boundary layers and corner singularities

Chang-Yeol Jung 1, and  Roger Temam 2,

1. 

Department of Mathematics, Arizona State University,Tempe, AZ 85287-1804, The Institute for Scientific Computing and Applied Mathematics, Indiana University, 831 E. 3rd St., Rawles Hall, Bloomington, IN 47405, United States
2. 

The Institute for Scientific Computing and Applied Mathematics, Indiana University, 831 E. 3rd St., Rawles Hall, Bloomington, IN 47405

Received  December 2007 Revised  May 2008 Published  September 2008

Our aim in this article is to study the interaction of\textit{boundary layers} and \textit{corner singularities} in thecontext of singularly perturbed convection-diffusion equations. Forthe problems under consideration, we determine a simplified form ofthe corner singularities and show how to use it for the numericalapproximation of such problems in the context of variationalapproximations using the concept of \textit{enriched spaces}.
Keywords: boundary layers; boundary layer element; finite elements; singularly perturbed problem; convection-diffusion.
Mathematics Subject Classification: Primary: 65N30, 34D15; Secondary: 76N20.
Citation: Chang-Yeol Jung, Roger Temam. Interaction of boundary layers and corner singularities. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 315-339. doi: 10.3934/dcds.2009.23.315
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