In this paper, we design and analyze a Hybrid-High Order (HHO) approximation for a class of quasilinear elliptic problems of nonmonotone type. The proposed method has several advantages, for instance, it supports arbitrary order of approximation and general polytopal meshes. The key ingredients involve local reconstruction and high-order stabilization terms. Existence and uniqueness of the discrete solution are shown by Brouwer's fixed point theorem and contraction result. A priori error estimate is shown in discrete energy norm that shows optimal order convergence rate. Numerical experiments are performed to substantiate the theoretical results.

翻译：在本文中,我们设计并分析非单体型准线性椭圆形问题类别的混合-高度命令近似值。例如,拟议方法具有若干优点,例如,它支持任意近似和一般多面藻类的近似和一般多面藻类。关键成分涉及当地的重建和高端稳定条件。布鲁韦尔的固定点理论和收缩结果显示了离散解决办法的存在和独特性。在显示最佳顺序趋同率的离散能源规范中显示了先验错误估计值。进行了数字实验以证实理论结果。