Finite Element Discretization in Time Direction
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?
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- Jayadeep U. B.'s blog
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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