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A note on robust exponential convergence of finite element methods for problems with boundary layers.

by J. M. Melenk

(Report number 1996-06)

Abstract
The emhp/em version of the finite element method for a one dimensional, singularly perturbed elliptic model problem with analytic right hand side is considered. It is shown that the use of piecewise polynomials of degree emp/em on a mesh consisting of three suitably chosen elements leads to robust exponential convergence, i.e., the rate of convergence depends only on the right hand side and is independent of the perturbation parameter.

Keywords: boundary layer, singularly perturbed problem, emp/em version, emhp/em version, spectral element method

@Techreport{M96_189,
  author = {J. M. Melenk},
  title = {A note on robust exponential convergence of finite element methods for problems with boundary layers.},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1996-06},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1996/1996-06.pdf },
  year = {1996}
}

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