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Two-sided bounds of the discretization error for finite elements
Published online by Cambridge University Press: 06 April 2011
Abstract
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.
- Type
- Research Article
- Information
- ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 5 , September 2011 , pp. 915 - 924
- Copyright
- © EDP Sciences, SMAI, 2011
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