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

10/29/2021
by   Thirupathi Gudi, et al.
0

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.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

12/09/2020

Improved error estimates for Hybrid High-Order discretizations of Leray-Lions problems

We derive novel error estimates for Hybrid High-Order (HHO) discretizati...
03/30/2020

A Hybrid High-Order method for creeping flows of non-Newtonian fluids

In this paper, we design and analyze a Hybrid High-Order discretization ...
01/21/2021

A priori and a posteriori error analysis of the lowest-order NCVEM for second-order linear indefinite elliptic problems

The nonconforming virtual element method (NCVEM) for the approximation o...
05/28/2020

A priori and a posteriori error analysis for the Nitsche's method of a reduced Landau-de Gennes problem

The equilibrium configurations of a two dimensional planar bistable nema...
10/20/2021

A C^0 interior penalty method for mth-Laplace equation

In this paper, we propose a C^0 interior penalty method for mth-Laplace ...
12/16/2019

A Control-Theoretic Perspective on Optimal High-Order Optimization

In this paper, we provide a control-theoretic perspective on optimal ten...
04/30/2021

Design and analysis of the Extended Hybrid High-Order method for the Poisson problem

We propose an Extended Hybrid High-Order scheme for the Poisson problem ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.