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中文摘要：
本文对具间断系数的二阶椭圆界面问题提出一种浸入有限元方法（the immersed finiteele—mentmethod），即在界面单元上采用依赖于界面的线性多项式空间离散，而在非界面单元上采用Crouzeix—Raviart非协调元离散．论证表明，该方法具有对界面问题解的最优L^2-模和H^1-模收敛精度．
英文摘要：
In this paper we present an immersed finite element method to solve numerically second order elliptic interface problems. The characteristics of the method is to prescribe a modi- fied linear finite element space on each interface element in order to enforce the flux jump condition on the smooth interface, and a Crouzeix-Raviart non-conforming element on each non-interface element. Optimal-order error estimates are derived in the broken H^1-norm and L^2-norm.
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