Motivated by the pricing of American options for baskets we
consider a parabolic variational inequality in a bounded
polyhedral domain $\Omega\subset\mathbb{R}^d$ 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 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.