We design a Hybrid High-Order (HHO) scheme for the Poisson problem that is fully robust on polytopal meshes in the presence of small edges/faces. We state general assumptions on the stabilisation terms involved in the scheme, under which optimal error estimates (in discrete and continuous energy norms, as well as $L^2$-norm) are established with multiplicative constants that do not depend on the maximum number of faces in each element, or the relative size between an element and its faces. We illustrate the error estimates through numerical simulations in 2D and 3D on meshes designed by agglomeration techniques (such meshes naturally have elements with a very large numbers of faces, and very small faces).
翻译:我们为Poisson问题设计了一个混合高级命令(HHO)计划,该计划在有小边缘/面孔的情况下在多顶层间贝上完全坚固。我们对这一计划所涉及的稳定条件作了一般假设,根据这个计划,最佳误差估计(在离散和连续的能源规范中,以及$L ⁇ 2美元-诺尔姆)是用不取决于每个元素的最大面孔或一个元素与其面孔的相对大小的倍增常数来设定的。我们通过以聚积技术设计的对介质进行2D和3D的数值模拟来说明误差估计(这些模类自然含有大量面孔和很小面孔的元素)。