We consider an elliptic variational inequality with unilateral constraints in
a Hilbert space X which, under appropriate assumptions on the data, has a
unique solution u. We formulate a convergence criterion to the solution u,
i.e., we provide necessary and sufficient conditions on a sequence
{unβ}βX which guarantee the convergence unββu in the space X.
Then, we illustrate the use of this criterion to recover well-known convergence
results and well-posedness results in the sense of Tykhonov and Levitin-Polyak.
We also provide two applications of our results, in the study of a heat
transfer problem and an elastic frictionless contact problem, respectively.Comment: 26 pages. arXiv admin note: text overlap with arXiv:2005.1178