A Hybrid-High Order Method for Quasilinear Elliptic Problems of Nonmonotone Type
Numerical Analysis
2021-11-01 v1 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.2110.15579,
title = {A Hybrid-High Order Method for Quasilinear Elliptic Problems of Nonmonotone Type},
author = {Thirupathi Gudi and Gouranga Mallik and Tamal Pramanick},
journal= {arXiv preprint arXiv:2110.15579},
year = {2021}
}