Geodesic
A posteriori error estimation for arbitrary order FEM applied to singularly perturbed one-dimensional reaction-diffusion problems
Applications of Mathematics, Tome 59 (2014) no. 3, pp. 241-256.

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FEM discretizations of arbitrary order $r$ are considered for a singularly perturbed one-dimensional reaction-diffusion problem whose solution exhibits strong layers. A posteriori error bounds of interpolation type are derived in the maximum norm. An adaptive algorithm is devised to resolve the boundary layers. Numerical experiments complement our theoretical results.
DOI : 10.1007/s10492-014-0052-8
Classification : 65L10, 65L11, 65L50, 65L60, 65L70
Keywords: reaction-diffusion problem; singular perturbation; mesh adaptation 
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     title = {A posteriori error estimation for arbitrary order {FEM} applied to singularly perturbed one-dimensional reaction-diffusion problems},
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Linß, Torsten. A posteriori error estimation for arbitrary order FEM applied to singularly perturbed one-dimensional reaction-diffusion problems. Applications of Mathematics, Tome 59 (2014) no. 3, pp. 241-256. doi : 10.1007/s10492-014-0052-8. http://geodesic.mathdoc.fr/articles/10.1007/s10492-014-0052-8/

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