Probabilistic analysis of an a posteriori error estimator for finite elements

Author (s): Díez, P. and Egozcue, J.J.
Journal: Mathematical Models and Methods in Applied Sciences

Volume: 11, Issue 5
Pages: 841 – 854
Date: 2001

A residual type a posteriori error estimator for finite elements is analyzed using a new technique. In this case, the error estimate is the result of two consecutive projections of the exact error on two finite-dimensional subspaces. The analysis introduced in this paper is based on a probabilistic approach, that is, the idea is to assess the average value of the effectivity index (the ratio estimated error over exact error) by assuming the randomness of the exact error. The average value characterizes the mean behavior of the estimator and it is found to be related with some geometric properties of the subspaces. These geometric properties are obtained from the standard matrices of the linear systems arising in the formulation of the finite element method.

Keywords: Error estimation; probabilistic analysis; finite elements; adaptivity



author = {D\'iez, Pedro and Egozcue, Juan Jos\'e},
title = {Probabilistic analysis of an "a posteriori" error estimator for finite elements},
journal = {Mathematical Models and Methods in Applied Sciences},
volume = {11},
number = {05},
pages = {841-854},
year = {2001},
doi = {10.1142/S0218202501001136},

URL = {http://www.worldscientific.com/doi/abs/10.1142/S0218202501001136},
eprint = {http://www.worldscientific.com/doi/pdf/10.1142/S0218202501001136}