  This paper gives some results related to the research problem about
infinite-dimensional affine variational inequalities raised by N.D. Yen and X.
Yang [Affine variational inequalities on normed spaces, J. Optim. Theory Appl.,
178 (2018), 36--55]. Namely, we obtain local error bounds for affine
variational inequalities on Hilbert spaces. To do so, we revisit two
fundamental properties of polyhedral mappings. Then, we prove a locally upper
Lipschitzian property of the inverse of the residual mapping of the
infinite-dimensional affine variational inequality under consideration.
Finally, we derive the desired local error bounds from that locally upper
Lipschitzian property.
