We propose a novel hybrid high-order method (HHO) to approximate singularly perturbed fourth-order PDEs on domains with a possibly curved boundary. The two key ideas in devising the method are the use of a Nitsche-type boundary penalty technique to weakly enforce the boundary conditions and a scaling of the weighting parameter in the stabilization operator that compares the singular perturbation parameter to the square of the local mesh size. With these ideas in hand, we derive stability and optimal error estimates over the whole range of values for the singular perturbation parameter, including the zero value for which a second-order elliptic problem is recovered. Numerical experiments illustrate the theoretical analysis.

翻译：我们建议一种新型混合高顺序方法(HHO),在可能有弯曲边界的域中,近似奇扰四级PDE。在设计该方法时,两个主要想法是使用尼采型边界惩罚技术来弱力执行边界条件,并缩小稳定操作员的加权参数,将单扰动参数与当地网格大小的平方进行对比。有了这些想法,我们获得了单扰动参数整个数值范围的稳定性和最佳误差估计,包括收回第二序椭圆问题的零值。数字实验说明了理论分析。