Geodesic
Two-sided bounds of the discretization error for finite elements
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 45 (2011) no. 5, pp. 915-924

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We derive an optimal lower bound of the interpolation error for linear finite elements on a bounded two-dimensional domain. Using the supercloseness between the linear interpolant of the true solution of an elliptic problem and its finite element solution on uniform partitions, we further obtain two-sided a priori bounds of the discretization error by means of the interpolation error. Two-sided bounds for bilinear finite elements are given as well. Numerical tests illustrate our theoretical analysis.

DOI : 10.1051/m2an/2011003
Classification : 65N30
Keywords: Lagrange finite elements, Céa's lemma, superconvergence, lower error estimates 
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     title = {Two-sided bounds of the discretization error for finite elements},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {915--924},
     publisher = {EDP-Sciences},
     volume = {45},
     number = {5},
     year = {2011},
     doi = {10.1051/m2an/2011003},
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     zbl = {1269.65113},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2011003/}
}
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Křížek, Michal; Roos, Hans-Goerg; Chen, Wei. Two-sided bounds of the discretization error for finite elements. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 45 (2011) no. 5, pp. 915-924. doi: 10.1051/m2an/2011003

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