论文标题
用于接口问题的本地修改的二阶有限元方法及其在2维度的实现
A locally modified second-order finite element method for interface problems and its implementation in 2 dimensions
论文作者
论文摘要
局部修改的有限元方法，该方法在[Frei，Richter：Sinum 52（2014），第1页中引入。 2315-2334]，是一种简单拟合的有限元方法，能够解决界面问题中的弱不连续性。该方法基于固定的结构化粗网格，然后将其完善为子元素以解决内部界面。 在这项工作中，我们使用接口元素中的等法方法将本地修改的有限元方法{在两个空间维度中}扩展到二阶。因此，我们需要注意所得的弯曲边缘不会导致退化子元素。我们证明了$ l^2 $ norm和离散的能量规范中的最佳先验错误估计。最后，我们提出数值示例以证实理论发现。
The locally modified finite element method, which is introduced in [Frei, Richter: SINUM 52(2014), p. 2315-2334], is a simple fitted finite element method that is able to resolve weak discontinuities in interface problems. The method is based on a fixed structured coarse mesh, which is then refined into sub-elements to resolve an interior interface. In this work, we extend the locally modified finite element method {in two space dimensions} to second order using an isoparametric approach in the interface elements. Thereby we need to take care that the resulting curved edges do not lead to degenerate sub-elements. We prove optimal a priori error estimates in the $L^2$-norm and in a discrete energy norm. Finally, we present numerical examples to substantiate the theoretical findings.
