Paper Info
Title
Finite Element Method for a Nonlocal Problem of Kirchhoff Type
Abstract
The nonlocal term in the nonlinear equations of Kirchhoff type causes difficulties when the equation is solved numerically by using the Newton-Raphson method. This is because the Jacobian of the Newton-Raphson method is full. In this article, the finite element system is replaced by an equivalent system for which the Jacobian is sparse. We derive quasi-optimal error estimates for the finite element method and demonstrate the results with numerical experiments.
Year
DOI
Venue
2012
10.1137/110822931
SIAM J. Numerical Analysis
Keywords
DocType
Volume
kirchhoff type,finite element system,quasi-optimal error estimate,numerical experiment,finite element method,nonlocal term,nonlinear equation,nonlocal problem,equivalent system,newton-raphson method,finite element,elliptic
Journal
50
Issue
ISSN
Citations 
2
0036-1429
7
PageRank 
References 
Authors
0.91
1
1
Name
Order
Citations
PageRank
Thirupathi Gudi113514.43