ABSTRACT
This chapter considers time finite element processes based on various methods of approximation for non-self-adjoint as well as non-linear time differential operators for ordinary differential equations (ODEs) in time. The mathematical details of the finite element processes in time for ODEs in time can be derived using classical methods of approximation in time but applying them for the discretization Ω¯tT $ \bar{\Omega }_{t}^{T} $ instead of the non-discretized domain Ω¯t $ \bar{\Omega }_{t} $ as done in classical methods. The chapter considers some illustrative model problems to demonstrate the details of various methods of approximation and the associated finite element processes based on integral forms in time. It then discusses numerical studies for a model problem using finite element process in time using least squares process (LSP) based on time residual functional. The element equations are established using the element map in the natural coordinate space.
