  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.
