In this article, we design and analyze a Hybrid High-Order (HHO) finite element approximation for a class of strongly nonlinear boundary value problems. We consider an HHO discretization for a suitable linearized problem and show its well-posedness using the Gardings type inequality. The essential ingredients for the HHO approximation involve local reconstruction and high-order stabilization. We establish the existence of a unique solution for the HHO approximation using the Brouwer fixed point theorem and contraction principle. We derive an optimal order a priori error estimate in the discrete energy norm. Numerical experiments are performed to illustrate the convergence histories.

翻译：本文设计并分析了一类强非线性边值问题的混合高阶（HHO）有限元逼近。我们考虑一个合适的线性化问题的HHO离散化，并利用Gardings型不等式证明其适定性。HHO逼近的基本要素包括局部重构和高阶稳定化。通过Brouwer不动点定理和压缩映射原理，我们证明了HHO逼近解的存在唯一性。在离散能量范数下，我们推导了最优阶先验误差估计。数值实验验证了收敛性结果。