Foundations of Computational Mathematics

, Volume 7, Issue 2, pp 245–269

Optimality of a Standard Adaptive Finite Element Method



In this paper an adaptive finite element method is constructed for solving elliptic equations that has optimal computational complexity. Whenever, for some s > 0, the solution can be approximated within a tolerance ε > 0 in energy norm by a continuous piecewise linear function on some partition with O(ε-1/s) triangles, and one knows how to approximate the right-hand side in the dual norm with the same rate with piecewise constants, then the adaptive method produces approximations that converge with this rate, taking a number of operations that is of the order of the number of triangles in the output partition. The method is similar in spirit to that from [SINUM, 38 (2000), pp. 466-488] by Morin, Nochetto, and Siebert, and so in particular it does not rely on a recurrent coarsening of the partitions. Although the Poisson equation in two dimensions with piecewise linear approximation is considered, the results generalize in several respects.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Society for the Foundations of Computational Mathematics 2006

Authors and Affiliations

  1. 1.Department of Mathematics, Utrecht UniversityThe Netherlands

Personalised recommendations