【摘要】 <正>1引言多孔介质中含两种及以上不同传导性或渗透率的一些物理模型,都可以由间断系数为张量的二阶椭圆界面方程来刻画.为了服从守恒律,界面方程的解必须满足界面跳跃条件.当界面线充分光滑时,解在各个子区域上也分别都是光滑的.但因为扩散系数沿界面发生间断,解的整体正则性比较低,通常的数值方法难以得到理想的逼近精度.多种数值实验表明界面浸入有限元(IIFE)方法对于求解这类椭圆界面问题十分有效.这是由于这种方法把界面跳跃条件强加在有限元空间中,故不需要沿界面进行网格剖分.更多还原

【Abstract】 In this paper,an immersed Crouzeix-Raviart finite element method is developed for solving elliptic interface problems with discontinuous tensorcoefficients.The immersed interface finite element(IIFE) spaces are constructed by standard linear Crouzeix-Raviart-type polynomials on non-interface triangular elements and piecewise linear Crouzeix-Raviart-type polynomials on interface elements,which both have edge averages as degrees of freedom.And the flux jump conditions are weakly enforced on the smooth interface.Numerical experiments are conducted to verify that the IIFE solutions possess optimal-order convergence in both the L~2-norm and broken H~1-norm.更多还原