TY - JOUR T1 - On Error Estimates of the Penalty Method for the Unsteady Conduction-Convection Problem I: Time Discretization JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 876 EP - 891 PY - 2012 DA - 2012/09 SN - 9 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/663.html KW - Unsteady conduction-convection problem, Penalty method, Time discretization, Optimal error estimates. AB -

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.