In this article, we design and analyze a hybrid high-order (HHO) finite element approximation for the solution of a nonlocal nonlinear problem of Kirchhoff type. The HHO method involves arbitrary-order polynomial approximations on structured and unstructured polytopal meshes. We establish the existence of a unique discrete solution to the nonlocal nonlinear discrete problem. We derive an optimal-order error estimate in the discrete energy norm. The discrete system is solved using Newton's iterations on the sparse matrix system. We perform numerical tests to substantiate the theoretical results.

翻译：本文针对一类基尔霍夫型非局部非线性问题，设计并分析了一种混合高阶（HHO）有限元近似方法。该HHO方法支持在结构化和非结构化多面体网格上采用任意阶多项式逼近。我们证明了该非局部非线性离散问题存在唯一离散解，并在离散能量范数下导出了最优阶误差估计。离散系统通过牛顿迭代法在稀疏矩阵系统上求解。我们进行了数值实验以验证理论结果。