ABSTRACT
In this chapter the authors consider space-time decoupled or quasi finite element formulation for initial value problems (IVPs). A numerical solution of the ODEs in time in variables {δ(t)} yielding evolution can be obtained using: time integration methods, explicit methods, implicit methods, direct methods, and finite element processes in time, often referred to as variational methods in time. The space-time decoupled approach inherently leads to a compromised physics in the resulting computational infrastructure in which the error introduced by decoupling space and time may not be recoverable by nonconcurrent refinements in space and time. The authors present various details of the space-time decoupled method of obtaining ODEs in time from the PDEs in space and time describing the evolutions. The authors then present details of spatial discretization, element equations, and the final assembled equations for the spatial discretization representing ODEs in time.
