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 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.
Cite
@article{arxiv.2309.13352,
title = {A Hybrid High-Order Method for a Class of Strongly Nonlinear Elliptic Boundary Value Problems},
author = {Gouranga Mallik and Thirupathi Gudi},
journal= {arXiv preprint arXiv:2309.13352},
year = {2023}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2110.15579