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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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|
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