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

TL;DR

This paper introduces a Hybrid-High Order method for solving complex quasilinear elliptic problems, supporting arbitrary approximation orders and general meshes, with proven stability, convergence, and validated by numerical tests.

Contribution

It presents a novel HHO approach for nonmonotone quasilinear elliptic problems, including stability analysis and optimal error estimates.

Findings

Supports arbitrary order approximation

Achieves optimal convergence rates

Numerical experiments confirm theoretical results

Abstract

In this paper, we design and analyze a Hybrid-High Order (HHO) approximation for a class of quasilinear elliptic problems of nonmonotone type. The proposed method has several advantages, for instance, it supports arbitrary order of approximation and general polytopal meshes. The key ingredients involve local reconstruction and high-order stabilization terms. Existence and uniqueness of the discrete solution are shown by Brouwer's fixed point theorem and contraction result. A priori error estimate is shown in discrete energy norm that shows optimal order convergence rate. Numerical experiments are performed to substantiate the theoretical results.