A posteriori error analysis for parabolic variational inequalities
ESAIM: Modélisation mathématique et analyse numérique, Volume 41 (2007) no. 3, pp. 485-511.

Motivated by the pricing of American options for baskets we consider a parabolic variational inequality in a bounded polyhedral domain Ω d 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 L 2 (0,T;H 1 (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.

DOI: 10.1051/m2an:2007029
Classification: 58E35, 65N15, 65N30
Keywords: a posteriori error analysis, finite element method, variational inequality, american option pricing
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     title = {A posteriori error analysis for parabolic variational inequalities},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {485--511},
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Moon, Kyoung-Sook; Nochetto, Ricardo H.; Petersdorff, Tobias Von; Zhang, Chen-Song. A posteriori error analysis for parabolic variational inequalities. ESAIM: Modélisation mathématique et analyse numérique, Volume 41 (2007) no. 3, pp. 485-511. doi : 10.1051/m2an:2007029. http://archive.numdam.org/articles/10.1051/m2an:2007029/

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