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error analysis for parabolic variational inequalities

Kyoung-Sook Moon; Ricardo H. Nochetto; Tobias von Petersdorff; Chen-song Zhang — 2007

ESAIM: Mathematical Modelling and Numerical Analysis

Motivated by the pricing of American options for baskets we consider a parabolic variational inequality in a bounded polyhedral domain $Ω \subset ℝ^{d}$ 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 error estimator and show that it gives an upper bound for the error in (Ω)). The error estimator is localized in the sense that the size of the elliptic residual is only relevant...

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