论文标题
高阶不融合杂交不连续的盖尔金方法，用于线性弹性
A high order unfitted hybridizable discontinuous Galerkin method for linear elasticity
论文作者
论文摘要
这项工作分析了针对域中的线性弹性问题不一定是多面体的高阶杂交不连续的Galerkin（HDG）方法。该结构域通过可以计算HDG解决方案的多面体计算域近似。将旋转作为未知数之一的引入使我们能够使用位移的梯度来获得计算域中边界数据的明确表示。边界数据通过线积分从真实边界传递到计算边界，在该边界中，积分取决于Cauchy应力张量和旋转。在计算和真实边界之间的紧密假设下，该方案被证明是良好的，即使在几乎不可压缩的情况下，也提供了最佳的误差估计。提出了二维的数值实验。
This work analyzes a high order hybridizable discontinuous Galerkin (HDG) method for the linear elasticity problem in a domain not necessarily polyhedral. The domain is approximated by a polyhedral computational domain where the HDG solution can be computed. The introduction of the rotation as one of the unknowns allows us to use the gradient of the displacements to obtain an explicit representation of the boundary data in the computational domain. The boundary data is transferred from the true boundary to the computational boundary by line integrals, where the integrand depends on the Cauchy stress tensor and the rotation. Under closeness assumptions between the computational and true boundaries, the scheme is shown to be well-posed and optimal error estimates are provided even in the nearly incompressible. Numerical experiments in two-dimensions are presented.
