Finite-element approximation of a fourth-order differential equation
โ Scribed by J.Y. Shin
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 298 KB
- Volume
- 35
- Category
- Article
- ISSN
- 0898-1221
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โฆ Synopsis
A finite-element approximation of a fourth-order differential equation is given. In the direct implementation, a system of nonlinear equations will be obtained and also a full size matrix will be introduced when Newton's method is adopted to solve the system. This difficulty can be avoided by the use of an iterative scheme which is shown to converge to the solution.
๐ SIMILAR VOLUMES
Finite-element approximations for a fourth-order differential equation based on the space of piecewise linear polynomials on the uniform grid are introduced. And error estimates for the approximation are also given.
In a recent paper (Mckee, 19751 the Hopscotch method was applied to solve the fourth-order parabolic (beam) equation. Several computational schemes were discussed which prove to be conditionally stable with the stability range no better than that of the usual explicit scheme. By using two different