Instead of the usual presentation given to the formulation of Initial Boundary Boundary Value Problems (IBVP), we do no take the partition of the continuous media directly to the limit of zero shrinking size concerning the spatial dimensions at any given time, which leads to some differential expression for the limiting net force upon the element. We consider each media element as a single particle evolving in “time” under a “force” represented by the discrete mimetic analog of the differential expression. We base our approach on a discrete extended Gauss’s divergence theorem, without using exterior calculus, to construct our mimetic operators combined with a symplectic integration scheme.