@Article{JCM-27-148,
author = {Dietrich Braess, Carsten Carstensen and Ronald H.W. Hoppe},
title = {Error Reduction in Adaptive Finite Element Approximations of Elliptic Obstacle Problems},
journal = {Journal of Computational Mathematics},
year = {2009},
volume = {27},
number = {2-3},
pages = {148--169},
abstract = {<p style="text-align: justify;">We consider an adaptive finite element method (AFEM) for obstacle problems associated
with linear second order elliptic boundary value problems and prove a reduction
in the energy norm of the discretization error which leads to R-linear convergence. This
result is shown to hold up to a consistency error due to the extension of the discrete
multipliers (point functionals) to $H^{−1}$ and a possible mismatch between the continuous
and discrete coincidence and noncoincidence sets. The AFEM is based on a residual-type
error estimator consisting of element and edge residuals. The a posteriori error analysis
reveals that the significant difference to the unconstrained case lies in the fact that these
residuals only have to be taken into account within the discrete noncoincidence set. The
proof of the error reduction property uses the reliability and the discrete local efficiency of
the estimator as well as a perturbed Galerkin orthogonality. Numerical results are given
illustrating the performance of the AFEM.</p>},
issn = {1991-7139},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jcm/8565.html}
}