We derive novel error estimates for Hybrid High-Order (HHO) discretizations of Leray–Lions problems set in \(W^{1,p}\) with \(p\in (1,2]\). Specifically, we prove that, depending on the degeneracy of the problem, the convergence rate may vary between \((k+1)(p-1)\) and \((k+1)\), with k denoting the degree of the HHO approximation. These regime-dependent error estimates are illustrated by a complete panel of numerical experiments.

中文翻译：

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Leray-Lions问题的混合高阶离散化的改进误差估计

我们推导了在\（W ^ {1，p} \）中设置为\（p \ in（1,2] \）的Leray–Lions问题的混合高阶（HHO）离散化的新颖误差估计。根据问题的简并性，收敛速度可能在\（（k + 1）（p-1）\）和\（（k + 1）\）之间变化，其中k表示HHO近似度这些完整的数值实验说明了这些依赖于制度的误差估计。