A Hybrid High-Order Finite Element Method for a Nonlocal Nonlinear Problem of Kirchhoff Type

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.