  In this article, a concept of implicit methods for scalar conservation laws
in one or more spatial dimensions allowing also for source terms of various
types is presented. This material is a significant extension of previous work
of the first author [3]. Implicit notions are developed that are centered
around a monotonicity criterion. We demonstrate a connection between a
numerical scheme and a discrete entropy inequality, which is based on a
classical approach by Crandall and Majda. Additionally, three implicit methods
are investigated using the developed notions. Next, we conduct a convergence
proof which is not based on a classical compactness argument. Finally, the
theoretical results are confirmed by various numerical tests.
