On Error Estimates of the Penalty Method for the Unsteady Conduction-Convection Problem I: Time Discretization

Abstract

In this paper, the penalty method is proposed and discussed for the unsteady conduction-convection problem in two dimensions. In addition, we analyze its time discretization which is based on the backward Euler implicit scheme. Finally, the main results of this paper that optimal error estimates are obtained for the penalty system and the time discretization under reasonable assumptions on the physical data.