Some $L_2$-error estimates for semi-variational method applied to parabolic equations

summary:The convergence of the semi-variational approximations to the solution of a mixed parabolic problem is investigated. The derivation of an estimate in $L_2$-norm follows the approach suggested by Dupont, using a parabolic regularity and a projection introduced by Bramble and Osborn. As a result, the second semi-variational approximation is found to possess the maximal possible order of accuracy in space and the fourth order in time