We propose an Extended Hybrid High-Order scheme for the Poisson problem with solution possessing weak singularities. Some general assumptions are stated on the nature of this singularity and the remaining part of the solution. The method is formulated by enriching the local polynomial spaces with appropriate singular functions. Via a detailed error analysis, the method is shown to converge optimally in both discrete and continuous energy norms. Some tests are conducted in two dimensions for singularities arising from irregular geometries in the domain. The numerical simulations illustrate the established error estimates, and show the method to be a significant improvement over a standard Hybrid High-Order method.

翻译：我们为Poisson问题提出了一个扩展混合高级命令计划,其解决方案具有微弱的单一性,一些一般性假设是对这一单一性的性质和解决方案的剩余部分作出说明。该方法的制定是通过以适当的单一功能丰富当地的多圆形空间。通过详细的错误分析,该方法在离散和连续的能源规范中都表现出最佳的趋同性。一些测试是按两个维度进行的,分别针对域内不规则的地理偏差产生的独特性。数字模拟显示了既定的误差估计数,并表明该方法比标准混合高圆形方法有显著的改进。