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

<cite authors="Roland Glowinski" mrnumber="737005" cite="ISBN: 0-387-12434-9">_Roland Glowinski_, MR 737005 [**Numerical methods for nonlinear variational problems**](http://dx.doi.org/10.1007/978-3-662-12613-4), ISBN: 0-387-12434-9.</cite>

(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

  <cite authors="Roland Glowinski, Jacques-Louis Lions, and Raymond Trémolières" mrnumber="1333916" cite="ISBN: 0-444-86199-8">_Roland Glowinski, Jacques-Louis Lions, and Raymond Trémolières_, MR 1333916 [**Numerical analysis of variational inequalities**](http://www.ams.org/mathscinet-getitem?mr=1333916), ISBN: 0-444-86199-8.</cite>

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