Abstract: It is discussed that the numerical approximation of interface problems for elliptic partial differential equations. For the interface problems with variable coefficients, it is introduced that a particular finite element method combined with the infinite element method to approach the singular solution in the neighborhood of the singular points, and it is proved that the method possesses the same accuracy as the finite element method to the regular solution. Numerical examples are also given.

Key words: infinite element method, interface problem, singularity

摘要： 讨论了椭圆型偏微分方程内边界问题的数值逼近。对变系数内边界问题，介绍了一种特殊的有限元方法。该方法结合了无限元方法，使在奇点附近的奇性解得到好的逼近。证明了该方法具有与有限元方法对正则解相同的精确度。最后给出了计算的实例。

关键词: 无限元方法, 内边界问题, 奇性