Gudi, Thirupathi (2012) Finite Element Method for a Nonlocal Problem of Kirchhoff Type SIAM Journal on Numerical Analysis, 50 (2). pp. 657-668. ISSN 0036-1429
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Official URL: https://doi.org/10.1137/110822931
Related URL: http://dx.doi.org/10.1137/110822931
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: | Article |
|---|---|
| Source: | Copyright of this article belongs to Society for Industrial and Applied Mathematics. |
| Keywords: | Finite Element; Nonlocal; Elliptic; Kirchhoff Equation |
| ID Code: | 141576 |
| Deposited On: | 02 Dec 2025 07:57 |
| Last Modified: | 02 Dec 2025 07:57 |
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