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Finite Element Method For A Nonlocal Problem Of Kirchhoff Type

Gudi, Thirupathi (2012) Finite Element Method For A Nonlocal Problem Of Kirchhoff Type. In: SIAM JOURNAL ON NUMERICAL ANALYSIS, 50 (2). pp. 657-668.

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Official URL: http://epubs.siam.org/toc/sjnaam/50/2

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.

Item Type: Journal Article
Additional Information: Copyright for this article belongs to Society for Industrial and Applied Mathematics
Keywords: finite element;nonlocal;elliptic;Kirchhoff equation
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 19 Jun 2012 11:20
Last Modified: 19 Jun 2012 11:33
URI: http://eprints.iisc.ernet.in/id/eprint/44558

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