On the solution of diffusion—convection equations by the space—time finite element method

A functional has been developed for the finite element solution of diffusion—convection problems. This functional is suitable for the application of the variational principle on discretization schemes in the space—time domain. This algorithm has shown to be computationally efficient over the conventional finite element discretization in the space domain alone. Numerical examples on one-dimensional energy transport have been included to illustrate the merit of this technique.