【摘要】 本文提出了一种求解椭圆界面问题的基于四边形网格的非协调匹配有限元方法,在界面划分的子区域允许用不同尺寸的网格.界面跳量条件由具有加权平均的加罚技术处理.本文得到了数值格式误差的最优收敛阶,能量范数的相对误差不依赖于网格尺寸的比值及不同系数的比值.最后,通过数值算例验证了理论分析.更多还原

【Abstract】 In this paper,a nonconforming fitted finite element method based on the rectangular mesh is proposed for elliptic interface problems,which allows to use different meshes in different sub-domains separated by the interface.The transmission conditions across the interface are treated by the penalty technique with some harmonic-weighted averages.Optimal order error estimates in energy norm and L~2-norm are proved for our scheme.In particular,the relative error estimate in energy norm is independent of the ratio of mesh sizes and the contrast of the discontinuous coefficients across the interface.Numerical examples are also provided to confirm the theoretical results.更多还原