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.

翻译：我们设计并分析$C$0的匹配混合高顺序(HHO)方法,用夹紧或简单支持的边界条件来近似双调问题。$C$0的匹配HHHO方法取决于细胞未知值,这些未知值相当于$C$0的匹配多义顺序(k+2)美元,这相当于网格单元格和面相异的混合混合混合混合高顺序($kge0)的解决方案的解决方案,大约相当于$K$0美元。这种方法为平滑解决方案提供$O(h ⁇ k+1})$HC$2$-eror估计数。错误分析中的一个重要新颖之处是降低精确解决方案的最低常规性要求。实现这一方法的适用范围大于仅仅$C$0的匹配HHHHHO方法,并且为了说明这一点,我们概述了对众所周知的异式加勒金(IPDG$0+1美元)对异式内装加勒金(IPDG$)的正常衍生法的错误分析。目前技术要求的气泡化方法或数字式格式,包括目前的HC格式格式,最后要求各种方法。