In the finite element analysis of a transient problem, the usual procedure is to discretize the space (domain) using finite elements, while in the time direction, a time-stepping scheme based on finite differences is used. Is it possible to use a finite element type discretization in time also? Is there any work done in this manner?
respond
if you use discontinuous galerkin method, you obtain a scheme that is higher order RK method. It is doable but have no practical value.
space-time finite elements
The space-time finite element formulation is what you're looking for. There are plenty of papers on this approach.
space-time intro
For a textbook introduction, try Claes Johnson's book "Numerical Solutions of Partial Differential Equations by the Finite Element Method".
Prof. Dr. Sanjay Govindjee
University of California, Berkeley
Hi, You may also refer
Hi,
You may also refer Zienkiewicz's book. It deals with temporal domain discretisation using FEM.
Regards,
- Ramadas