ABSTRACT
This chapter considers stability analysis of the space-time coupled finite element methods of approximation for initial value problems (IVPs) as well as space-time decoupled finite element methods of approximation for IVPs. In space-time coupled methods simultaneous dependence of the dependent variables on space and time is preserved. The space-time finite element method derives its theoretical foundation from the classical space-time coupled methods of approximation in which the space-time domain is not discretized. Calculus of variations of space-time functionals permits development of the theoretical foundation for obtaining approximate solutions of IVPs using space-time coupled methodology. The chapter considers mathematical classification of all space-time differential operators into non-self-adjoint and non-linear space-time operators. For this classification it focuses on STGTM, STPGM, STWRM, STGM/WF, and STLSP methods of approximation and determines space-time variational consistency or space-time variational inconsistency of the resulting space-time integral forms.
