The Finite Element Method for Initial Value Problems : Mathematics and Computations

Unlike most finite element books that cover time dependent processes (IVPs) in a cursory manner, The Finite Element Method for Initial Value Problems: Mathematics and Computations focuses on the mathematical details as well as applications of space-time coupled and space-time decoupled finite element methods for IVPs.

Space-time operator classification, space-time methods of approximation, and space-time calculus of variations are used to establish unconditional stability of space-time methods during the evolution.

Space-time decoupled methods are also presented with the same rigor.

Stability of space-time decoupled methods, time integration of ODEs including the finite element method in time are presented in detail with applications.

Modal basis, normal mode synthesis techniques, error estimation, and a posteriori error computations for space-time coupled as well as space-time decoupled methods are presented.

This book is aimed at a second-semester graduate level course in FEM.