Error Estimates Under Minimal Regularity for Single Step Finite Element Approximations of Parabolic Partial Differential Equations

Abstract

This paper studies error estimations for a fully discrete, single step finite element scheme for linear parabolic partial differential equations. Convergence in the norm of the solution space is shown and various error estimates in this norm are derived. In contrast to like results in the extant literature, the error estimates are derived in a stronger norm and under minimal regularity assumptions.