We consider variational inequalities with different trial and test spaces and a possibly non- coercive bilinear form. Well-posedness could be achieved under general conditions that are e.g. valid for the space-time formulation of parabolic variational inequalities. As an example for a parabolic variational inequality, we may think about time-dependent obstacle problems or option pricing, e.g. for American Options or Swing Options.
Fine discretizations that are needed for such problems resolve in high dimensional problems and thus in long computing times. To reduce the dimensionality of these problems, we use the Reduced Basis Method.
In our work, error estimators in terms of the residual could be obtained by combining the Reduced Basis Method with a space-time formulation of the variational inequality. We provide numerical results for a heat inequality model focusing on rigorosity and efficiency of the error estimator.