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The hp finite element method for problems in mechanics with boundary layers

by Ch. Schwab and M. Suri and X. Xenophontos

(Report number 1996-20)

Abstract
We consider the numerical approximation of boundary layer phenomena occuring 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 exisiting, commercial emp/em and emhp/em 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 emhp/em mesh design principles for situations where both corner singularities and boundary layers are present.

Keywords:

@Techreport{SSX96_203,
  author = {Ch. Schwab and M. Suri and X. Xenophontos},
  title = {The hp finite element method for problems in mechanics with boundary layers},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1996-20},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1996/1996-20.pdf },
  year = {1996}
}

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