A Hybrid High-Order Method for a Class of Strongly Nonlinear Elliptic Boundary Value Problems

Abstract

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 Gårding 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.Keywords Hybrid high-order methods • Second-order nonlinear elliptic problems • Brouwer fixed point theorem • Error estimates