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lagrange finite elements

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Two-sided bounds of the discretization error for finite elements
Michal Křížek, Hans-Goerg Roos, Wei Chen
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 45 / Issue 5 / September 2011

Published online by Cambridge University Press:

06 April 2011, pp. 915-924

Print publication:

September 2011
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We derive an optimal lower bound of theinterpolation error for linear finite elements on a bounded two-dimensionaldomain. Using the supercloseness between the linear interpolantof the true solution of an elliptic problem and its finite elementsolution on uniform partitions, we furtherobtain two-sided a priori bounds of the discretization error by means of theinterpolation error. Two-sided bounds for bilinear finite elementsare given as well. Numerical tests illustrate our theoreticalanalysis.