标题： 一种非协调浸入有限元方法用于椭圆界面问题 显示英文标题

标题： A nonconforming immersed finite element method for elliptic interface problems

摘要： 一种新的浸入有限元（IFE）方法用于具有不连续扩散系数的二阶椭圆问题。 IFE空间是基于带有积分自由度的旋转Q1非协调有限元构造的。 在该IFE方法中采用标准的非协调Galerkin方法，没有任何惩罚稳定项。 能量范数和L2范数的误差估计分别优于$O(h\sqrt{|\log h|})$和$O(h^2|\log h|)$，其中对数因子反映了跳跃不连续性。 报告了数值结果以确认我们的分析。 显示英文摘要

摘要： A new immersed finite element (IFE) method is developed for second-order elliptic problems with discontinuous diffusion coefficient. The IFE space is constructed based on the rotated Q1 nonconforming finite elements with the integral-value degrees of freedom. The standard nonconforming Galerkin method is employed in this IFE method without any penalty stabilization term. Error estimates in energy and L2 norms are proved to be better than $O(h\sqrt{|\log h|})$ and $O(h^2|\log h|)$, respectively, where the logarithm factors reflect jump discontinuity. Numerical results are reported to confirm our analysis.