ISSN:
1573-7691
Keywords:
finite element approximation
;
variational inequalities
;
a posteriori error estimators
;
obstacle problems
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
Notes:
Abstract In this paper, we present an a posteriori error analysis for the finite element approximation of a variational inequality. We derive a posteriori error estimators of residual type, which are shown to provide upper bounds on the discretization error for a class of variational inequalities provided the solutions are sufficiently regular. Furthermore we derive sharp a posteriori error estimators with both lower and upper error bounds for a subclass of the obstacle problem which are frequently met in many physical models. For sufficiently regular solutions, these estimates are shown to be equivalent to the discretization error in an energy type norm. Our numerical tests show that these sharp error estimators are both reliable and efficient in guiding mesh adaptivity for computing the free boundaries.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1011130501691
