论文标题
$ c^0 $ - 杂交高级方法
$C^0$-hybrid high-order methods for biharmonic problems
论文作者
论文摘要
我们设计和分析$ c^0 $ - 包含混合高阶（HHO）方法，以近似夹紧或简单支持的边界条件近似Biharmonic问题。 $ c^0 $ - 对hho方法的铰链铰链在$ c^0 $ - 控件$（k+2）$（k+2）$中的多项式（近似于网格单元格中的解决方案）和face notnomials中的解决方案，这是$ k \ ge0 $ ge0 $近似于Mesh Shemeleton上的正常衍生物。这样的方法传递$ O（H^{K+1}）$ $ H^2 $ -ERROR估算平滑解决方案。误差分析中的一个重要新颖性是降低精确解决方案的最低规律性要求。实现此目的的技术的适用性更广，不仅是$ c^0 $ - 包含HHO方法，为了说明这一点，我们概述了众所周知的$ C^0 $ - 包含内部罚款不连续的Galerkin（IPDG）方法的错误分析。目前的技术不需要气泡功能或$ c^1 $ -SMOOTHORE来评估右侧的右侧。最后，数值结果包括与各种现有方法的比较，展示了所提出的$ c^0 $ - 合格HHO方法的效率。
We devise and analyze $C^0$-conforming hybrid high-order (HHO) methods to approximate biharmonic problems with either clamped or simply supported boundary conditions. $C^0$-conforming HHO methods hinge on cell unknowns which are $C^0$-conforming polynomials of order $(k+2)$ approximating the solution in the mesh cells and on face unknowns which are polynomials of order $k\ge0$ approximating the normal derivative of the solution on the mesh skeleton. Such methods deliver $O(h^{k+1})$ $H^2$-error estimates for smooth solutions. An important novelty in the error analysis is to lower the minimal regularity requirement on the exact solution. The technique to achieve this has broader applicability than just $C^0$-conforming HHO methods, and to illustrate this point, we outline the error analysis for the well-known $C^0$-conforming interior penalty discontinuous Galerkin (IPDG) methods as well. The present technique does not require bubble functions or a $C^1$-smoother to evaluate the right-hand side in case of rough loads. Finally, numerical results including comparisons to various existing methods showcase the efficiency of the proposed $C^0$-conforming HHO methods.
