A New Technique for Error Analysis of Finite Element Approximations of Parabolic Problems with Non-smooth Initial Data

We propose a new technique for analyzing the error of finite element approximations of parabolic problems with non-smooth initial data. For homogeneous equation we prove optimal L-error estimate of order O ( h/t ) for t > 0 when the given initial data is in L. Further, for non-homogeneous parabolic equation with zero initial data we establish an optimal error estimate of order O(h) in L. Thus, we get the results of Luskin and Rannacher from [6] by a new technique that does not require error estimates in negative Sobolev norms.