论文标题
构建不连续的富集功能，以富集FEM的界面椭圆形问题1D
Construction of Discontinuous Enrichment Functions for Enriched FEM's for Interface Elliptic Problems in 1D
论文作者
论文摘要
我们引入了一种富集的未有限元方法，以解决不连续的解决方案的1D椭圆界面问题，包括具有隐式或罗宾型接口跳跃条件的解决方案。我们提出了一种新型的方法，可以通过找到不连续的解决方案的最佳订单插值函数来构建不连续的富集功能的单参数家族。在文献中，通常会事先给出富集功能，与插值操作员的构造步骤无关。此外，当参数设置为零时，我们恢复了众所周知的连续富集函数。为了证明其效率，将富集的线性和二次元素应用于多层壁模型，用于洗脱式支架，其中零升合跳跃条件和隐式浓度界面条件都存在。
We introduce an enriched unfitted finite element method to solve 1D elliptic interface problems with discontinuous solutions, including those having implicit or Robin-type interface jump conditions. We present a novel approach to construct a one-parameter family of discontinuous enrichment functions by finding an optimal order interpolating function to the discontinuous solutions. In the literature, an enrichment function is usually given beforehand, not related to the construction step of an interpolation operator. Furthermore, we recover the well-known continuous enrichment function when the parameter is set to zero. To prove its efficiency, the enriched linear and quadratic elements are applied to a multi-layer wall model for drug-eluting stents in which zero-flux jump conditions and implicit concentration interface conditions are both present.
