论文标题
线性弹性问题的界面/边界未配置的扩展高清方法
An interface/boundary-unfitted eXtended HDG method for linear elasticity problems
论文作者
论文摘要
关于接口和域边界上未固定网格上的线性弹性接口问题，提出了一种任意顺序的界面/边界未拟合的扩展杂交不连续的盖尔金（X-HDG）的任意顺序方法。该方法分别使用度的分段多项式$ k \（> = 1）$和$ k-1 $，分别用于界面内部元素内部元素内部的位移和压力近似值，以及在域间界面和域间界面上的数值$ k $的分段$ k $ $ k $的分段$ k $。 $ l^2 $ norm中的最佳错误估计值是为压力和位移而得出的。最后，数值实验证实了理论结果，并表明该方法还适用于裂纹尖端域的情况。
An interface/boundary-unfitted eXtended hybridizable discontinuous Galerkin (X-HDG) method of arbitrary order is proposed for linear elasticity interface problems on unfitted meshes with respect to the interface and domain boundary. The method uses piecewise polynomials of degrees $k\ (>= 1)$ and $k-1$ respectively for the displacement and stress approximations in the interior of elements inside the subdomains separated by the interface, and piecewise polynomials of degree $k$ for the numerical traces of the displacement on the inter-element boundaries inside the subdomains and on the interface/boundary of the domain. Optimal error estimates in $L^2$-norm for the stress and displacement are derived. Finally, numerical experiments confirm the theoretical results and show that the method also applies to the case of crack-tip domain.
