Poisson问题的扩展混合高阶方法的设计与分析
Design and analysis of the Extended Hybrid High-Order method for the Poisson problem
摘要：
对具有弱奇性解的Poisson问题提出了一种扩展的混合高阶格式。一些一般性的假设，说明这个奇点的性质和解决方案的其余部分。该方法是制定丰富的局部多项式空间与适当的奇异函数。通过详细的误差分析，该方法被证明是最佳收敛在离散和连续的能量范数。一些测试进行了在两个维度的奇异性所产生的不规则的几何形状的域。数值模拟说明了所建立的误差估计，并显示该方法是一个显着的改进，一个标准的混合高阶方法。
英文摘要：
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.
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