Virtual element method for the quasilinear convection-diffusion-reaction equation on polygonal meshes

In this paper, we analyze the virtual element method for the quasilinear convection-diffusion-reaction equation. The most important part in the analysis is the proof of existence and uniqueness of the branch of solution of the discrete problem. We extend the explicit analysis given by Lube ( Numer....

Full description

Saved in:
Bibliographic Details
Published in:Advances in computational mathematics 2022-12, Vol.48 (6), Article 78
Main Authors: Arrutselvi, M., Natarajan, E., Natarajan, S.
Format: Article
Language:English
Subjects:
Computational mathematics
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Convection-diffusion equation
Diffusion
Grid method
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Nonlinear equations
Reaction-diffusion equations
Visualization
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we analyze the virtual element method for the quasilinear convection-diffusion-reaction equation. The most important part in the analysis is the proof of existence and uniqueness of the branch of solution of the discrete problem. We extend the explicit analysis given by Lube ( Numer. Math. 61 , 335–357, 1992 ) for the finite element discretization to virtual element framework. We prove the optimal rate of convergence in the energy norm. In order to reduce the overall computational cost incurred for the nonlinear equations, we have performed the numerical experiments using a two-grid method. We validate the theoretical estimates with the computed numerical results.
ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-022-09990-y