The hp finite element method for problems in mechanics with boundary layers
Date
1998Source
Proceedings of the 1996 7th Conference on Numerical Methods and Computational Mechanics in Science and Engineering, NMCM 96Volume
157Issue
3-4Pages
311-333Google Scholar check
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Boundary layer phenomena are well-known in the study of fluid flow problems. Perhaps less known, but equally ubiquitous, is their existence in thermal, plate and shell analysis, where they also play a very significant role. In this paper, we will discuss the properties of boundary layers occurring in problems of plate and shell modeling, and in heat transfer, and address the question of their effective numerical resolution by the hp finite element method. We consider the numerical approximation of boundary layer phenomena occurring in many singularly perturbed problems in mechanics, such as plate and shell problems. We present guidelines for the effective resolution of such layers in the context of existing, commercial p and hp finite element (FE) version codes. We show that if high order, `spectral' elements are available, then just two elements are sufficient to approximate these layers at a near-exponential rate, independently of the problem parameters thickness or Reynolds number. We present hp mesh design principles for situations where both corner singularities and boundary layers are present.