带对流的稳态Stefan问题的有限元逼近

关于带有对流情形的稳态Stefan问题,其中假设液相部分的流动由Stokes方程确定,Canon,DiBennedetto,Knightly曾作过理论研究.本文将讨论其有限元逼近问题,并且得到了在合理正则性假设下的误差估计.

FINITE ELEMENT APPROXIMATIONS FOR THE STEADY STATE STEFAN PROBLEM WITH CONVECTION

In this paper the finite element approximations are studied for steady-state Stefan pro-blem with convection in the fluid phase governed by the Stokes equations and with adherenceof tbe fluid on all boundavies. The discrete schemes are given via the introduction of a tem-perature dependent penalty term in the fluid flow equation. The error estimates of the app-roximate solutions are derived under realistic regularity assumptions.