Two-grid virtual element discretization of quasilinear elliptic problem

In this paper a two grid algorithm for quasilinear elliptic problem based on virtual element method (VEM) discretization is proposed. With this new algorithm the solution of a quasilinear elliptic problem on a fine grid is reduced to the solution of a quasilinear elliptic problem on a much coarser g...

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Bibliographic Details
Published in:Mathematical modelling and analysis Vol. 29; no. 1; pp. 77 - 89
Main Authors: Chen, Fengxin, Yang, Minghui, Zhou, Zhaojie
Format: Journal Article
Language:English
Published: Vilnius Vilnius Gediminas Technical University 23.02.2024
Subjects:
a priori error estimate
Algorithms
Approximation
Discretization
Error analysis
Finite element analysis
Methods
Partial differential equations
Polynomials
two grid algorithm
virtual element method
virtual element method
two grid algorithm
a priori error estimate
ISSN:1392-6292, 1648-3510
Online Access:Get full text
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Summary:In this paper a two grid algorithm for quasilinear elliptic problem based on virtual element method (VEM) discretization is proposed. With this new algorithm the solution of a quasilinear elliptic problem on a fine grid is reduced to the solution of a quasilinear elliptic problem on a much coarser grid, and the solution of a linear system on the fine grid. A priori error estimate in H1 norm is derived. Numerical experiments are carried out to illustrate the theoretical findings.
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ISSN:1392-6292
1648-3510
DOI:10.3846/mma.2024.17745