Geodesic
Error estimates in balanced norms of finite element methods on Shishkin meshes for reaction-diffusion problems
Modelirovanie i analiz informacionnyh sistem, Tome 23 (2016) no. 3, pp. 357-363

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Error estimates of finite element methods for reaction-diffusion problems are often realized in the related energy norm. In the singularly perturbed case, however, this norm is not adequate. A different scaling of the $H^1$ seminorm leads to a balanced norm which reflects the layer behavior correctly.
Keywords: supercloseness, balanced norms.
Mots-clés : singular perturbation, combination technique 
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     author = {H.-G. Roos},
     title = {Error estimates in balanced norms of finite element methods on {Shishkin} meshes for reaction-diffusion problems},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {357--363},
     publisher = {mathdoc},
     volume = {23},
     number = {3},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2016_23_3_a12/}
}
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H.-G. Roos. Error estimates in balanced norms of finite element methods on Shishkin meshes for reaction-diffusion problems. Modelirovanie i analiz informacionnyh sistem, Tome 23 (2016) no. 3, pp. 357-363. http://geodesic.mathdoc.fr/item/MAIS_2016_23_3_a12/