A Hybrid High-Order Method for Quasilinear Elliptic Problems of Nonmonotone Type

Abstract

In this paper, we design and analyze a hybrid high-order approximation for a class of quasilinear elliptic problems of nonmonotone type. The proposed method has several advantages; for instance, it supports an arbitrary order of approximation and general polytopal meshes. The key ingredients involve local reconstruction and high-order stabilization terms. The existence of a unique discrete solution is shown by using Brouwer's fixed point theorem and the contraction principle. A priori error estimation is derived in a discrete energy norm that shows optimal order of convergence. Numerical experiments are performed to substantiate the theoretical results.