This is covered for example in Chapter III of

Roland Glowinski, MR 737005 Numerical methods for nonlinear variational problems, ISBN: 0-387-12434-9.

There is also a reprint of this book from 2008.

There's an overview of available schemes in chapter III of

Roland Glowinski, MR 737005 Numerical methods for nonlinear variational problems, ISBN: 0-387-12434-9.

(of which there is also reprint from 2008). The schemes are presented and a few references for their behaviour are given. In particular, this book references chapter 6 of

Roland Glowinski, Jacques-Louis Lions, and Raymond Trémolières, MR 1333916 Numerical analysis of variational inequalities, ISBN: 0-444-86199-8.

which might take you further, even though at a first glance I didn't see the explicit Euler method covered.