A posteriori error estimation in finite element analysis
- Mark Ainsworth”t
This paper reviews the important concepts presented by Trefftz in 1926 regarding bounds to solutions, error estimation, and hybrid fields for use with domain decomposition. Observations are offered from the perspective of today’s relatively mature state of the art in finite element methods. The numerical examples presented by Trefftz are also reviewed with the benefit of ‘exact’ solutions made available from current commercial finite element methods. The accuracies of the solutions given by Trefftz are quantified and compared, and the effectivity indices of Trefftz’s proposed error estimates are also quantified. An English translation of the original German version of Trefftz’s paper is included for reference in an Appendix.