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.

MSC codes

  1. 65N12
  2. 65N15
  3. 65N30

Keywords

  1. finite element
  2. nonlocal
  3. elliptic
  4. Kirchhoff equation

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Published In

cover image SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Pages: 657 - 668
ISSN (online): 1095-7170

History

Submitted: 31 January 2011
Accepted: 9 December 2011
Published online: 10 April 2012

MSC codes

  1. 65N12
  2. 65N15
  3. 65N30

Keywords

  1. finite element
  2. nonlocal
  3. elliptic
  4. Kirchhoff equation

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