Volume 41, Number 3, May-June 2007
|Page(s)||485 - 511|
|Published online||02 August 2007|
A posteriori error analysis for parabolic variational inequalities
Department of Mathematics and Information,
Kyungwon University, Bokjeong-dong, Sujeong-gu, Seongnam-si, Gyeonggi-do, 461-701, Korea. firstname.lastname@example.org
2 Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA. email@example.com
3 Department of Mathematics, University of Maryland, College Park, MD 20742, USA. firstname.lastname@example.org; email@example.com
Motivated by the pricing of American options for baskets we consider a parabolic variational inequality in a bounded polyhedral domain with a continuous piecewise smooth obstacle. We formulate a fully discrete method by using piecewise linear finite elements in space and the backward Euler method in time. We define an a posteriori error estimator and show that it gives an upper bound for the error in L2(0,T;H1(Ω)). The error estimator is localized in the sense that the size of the elliptic residual is only relevant in the approximate non-contact region, and the approximability of the obstacle is only relevant in the approximate contact region. We also obtain lower bound results for the space error indicators in the non-contact region, and for the time error estimator. Numerical results for d=1,2 show that the error estimator decays with the same rate as the actual error when the space meshsize h and the time step τ tend to zero. Also, the error indicators capture the correct behavior of the errors in both the contact and the non-contact regions.
Mathematics Subject Classification: 58E35 / 65N15 / 65N30
Key words: A posteriori error analysis / finite element method / variational inequality / American option pricing.
© EDP Sciences, SMAI, 2007
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.