New suitable finite element interpolation function is presented for solving unsteady problems, which provides a new and rigorous theoretical basis for the full time-space FE analysis of these problems.

Unfortunately, the existing time/space FEM is quite complicated, and difficult to be put into engineering use.

A refined space-time finite element method with moving grid for the parabolic equation;

Because of the calculation difficulty when solving the dynamic problems, development of the efficient algorithm for the dynamic differential equations is always an important research and the space-time finite element method can provide a feasible approach to it.

Based on the Gurtin variational principle, the formula of space time finite element method for transient heat conduction equation were derived.

The functional of heat conduction equation fitting for space time finite element method is derived.

Discussed in this paper is the space time finite element method for Navier stokes equations.

An adaptive space-time finite element method,continuous in space but discontinuous in time,for a class of semi-linear singular parabolic problem is investigated based on a combination of finite element and finite difference techniques.

Adaptive space-time finite element method,continuous in space but discontin- uous in time for a semilinear parabolic integro-differential equation is discussed.

Discontinuous space-time finite element methods deal with the spatial and the temporal variables conformably .