DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR PARABOLIC EQUATION

H. Kaneko, G. J. W. Hou and K. S. Bey

abstract:
In this paper, we develop a time and its corresponding spatial
discretization
scheme, based upon the  assumption of certain weak singularity of
$\|u_t\|_2$,
for the discontinuous Galerkin finite element method for one-dimensional
parabolic problems. Optimal convergence rates in both time and spatial
variables are obtained.