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.
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},
     journal = {Applications of Mathematics},
     pages = {241--256},
     year = {2014},
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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

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