%0 Journal Article
%T THE MIXED LEAST-SQUARE AND CHARACTERISTIC FINITE ELEMENT METHODS FOR TWO-PHASE DISPLACEMENT IN POROUS MEDIA<br>多孔介质驱动问题的混合元最小二乘特征有限元方法及其收敛分析
%A Zhao Weidong
%A <br>赵卫东
%J 计算数学
%D 2000
%I 
%X The mathematical model for two-phase displacement in porous media is a coupled initial boundary value problem of nonlinear partial differential equations which consist of a pressure equation and a saturation equation. In this paper, the mixed least-square weak form of pressure equation is got, and the positive definite characteristics of the weak form is proved. Based on this weak form, a new kind of numerical methods for two-phase displacement problems is proposed: the mixed least-square finite element method is used to solve pressure and Darcy velocity, and the saturation is solved by using characteristic finite element method. The main merits of the mixed least-square finite element method compared with mixed finite element method are: first, the structure of the mixed least-square finite el- ement spaces is just standard finite element spaces, it is simple and easy to use; second, the weak form of the mixed least-square finite element method for pressure is symetric and definite positive, thus there are many efficient methods to solve numerically; and the last, the Darcy velocity solved by mixed least-square finite element method is continuous. In numerical analyses, a very important inequality is obtained which is used to control the errors of the pressure and Darcy velocity, and the optimal error estomates of the proposed method are proved.
%K Two-phase displacement
%K mixed least-square finite
%K element
%K Characteristic finite element
%K error estimate<br>混合元最小二乘
%K 特征有限元
%K 多孔介质
%K 驱动问题
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=CC77F3CEF526D9CF0B3021650FB4E57E&aid=F1C4D221D5342CCF&yid=9806D0D4EAA9BED3&vid=BC12EA701C895178&iid=CA4FD0336C81A37A&sid=06EA2770E96C5402&eid=6700D0D256586E73&journal_id=0254-7791&journal_name=计算数学&referenced_num=0&reference_num=4