Two-sided bounds of the discretization error for finite elements
Michal Křížek, Hans-Goerg Roos, Wei Chen (2011)
ESAIM: Mathematical Modelling and Numerical Analysis
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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 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. ...