Mixed approximation of eigenvalue problems : a superconvergence result
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 43 (2009) no. 5, p. 853-865

We state a superconvergence result for the lowest order Raviart-Thomas approximation of eigenvalue problems. It is known that a similar superconvergence result holds for the mixed approximation of Laplace problem; here we introduce a new proof, since the one given for the source problem cannot be generalized in a straightforward way to the eigenvalue problem. Numerical experiments confirm the superconvergence property and suggest that it also holds for the lowest order Brezzi-Douglas-Marini approximation.

DOI : https://doi.org/10.1051/m2an/2009005
Classification:  65N25,  65N30,  65Q60
Keywords: eigenvalue problem, mixed finite element, superconvergence result
@article{M2AN_2009__43_5_853_0,
     author = {Gardini, Francesca},
     title = {Mixed approximation of eigenvalue problems : a superconvergence result},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {5},
     year = {2009},
     pages = {853-865},
     doi = {10.1051/m2an/2009005},
     zbl = {pre05608354},
     mrnumber = {2559736},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2009__43_5_853_0}
}
Gardini, Francesca. Mixed approximation of eigenvalue problems : a superconvergence result. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 43 (2009) no. 5, pp. 853-865. doi : 10.1051/m2an/2009005. http://www.numdam.org/item/M2AN_2009__43_5_853_0/

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