Non-smooth initial data error estimates with the weight norms for the linear finite element method of parabolic partial differential equations

摘要

We analyze the Galerkin approximation of a parabolic equation. For the second-order continuous time method with initial data only in L2, we prove an optimal order error estimate with weight norm. Our analysis uses elementary energy techniques and spectral representations and weight function techniques; the same techniques are shown to give an analysis of the Galerkin method time discretization.