  In infinite-dimensional Hilbert spaces we device a class of strongly
convergent primal-dual schemes for solving variational inequalities defined by
a Lipschitz continuous and pseudomonote map. Our novel numerical scheme is
based on Tseng's forward-backward-forward scheme, which is known to display
weak convergence, unless very strong global monotonicity assumptions are made
on the involved operators. We provide a simple augmentation of this algorithm
which is computationally cheap and still guarantees strong convergence to a
minimal norm solution of the underlying problem. We provide an adaptive
extension of the algorithm, freeing us from requiring knowledge of the global
Lipschitz constant. We test the performance of the algorithm in the
computationally challenging task to find dynamic user equilibria in traffic
networks and verify that our scheme is at least competitive to state-of-the-art
solvers, and in some case even improve upon them.
