A higher order nonconforming virtual element method for the Cahn-Hilliard equation

11/22/2021
by   Andreas Dedner, et al.
0

In this paper we develop a fully nonconforming virtual element method (VEM) of arbitrary approximation order for the two dimensional Cahn-Hilliard equation. We carry out the error analysis for the continuous-in-time scheme and verify the theoretical convergence result via numerical experiments. We present a fully discrete scheme which uses a convex splitting Runge-Kutta method to discretize in the temporal variable alongside the virtual element spatial discretization.

READ FULL TEXT

page 19

page 21

research
02/04/2022

Convergence Analysis of Virtual Element Method for Nonlinear Nonlocal Dynamic Plate Equation

In this article, we have considered a nonlinear nonlocal time dependent ...
research
03/27/2023

The nonconforming virtual element method with curved edges

We introduce a nonconforming virtual element method for the Poisson equa...
research
09/25/2022

A fully-discrete virtual element method for the nonstationary Boussinesq equations

In the present work we propose and analyze a fully coupled virtual eleme...
research
12/11/2019

Virtual element method for semilinear sine-Gordon equation over polygonal mesh using product approximation technique

In this paper, we employ the linear virtual element spaces to discretize...
research
07/29/2023

A C^1-conforming arbitrary-order two-dimensional virtual element method for the fourth-order phase-field equation

We present a two-dimensional conforming virtual element method for the f...
research
09/23/2022

Mixed Virtual Element approximation of linear acoustic wave equation

We design a Mixed Virtual Element Method for the approximated solution t...
research
12/31/2021

C^1-VEM for some variants of the Cahn-Hilliard equation: a numerical exploration

We consider the C^1-Virtual Element Method (VEM) for the conforming nume...

Please sign up or login with your details

Forgot password? Click here to reset