The Einstein Field Equations are a system of nonlinear, coupled partial differential equations. Their properties generally depend on the choice of gauge we use to write them explicitly. This makes the general initial value problems, or initial-boundary value problems, hard to solve analytically. Here numerical methods become important. My work pertains to regularizing schemes for the Einstein Field Equations and deriving suitable numerical schemes that in some sense assure stability of such initial value problems, or initial-boundary value problems, when evolved numerically.