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Finite-element approximation of a fourth-order differential equation

โœ 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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โœฆ 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.


๐Ÿ“œ SIMILAR VOLUMES


Error estimates of finite-element approx
โœ M.R. Ohm; H.Y. Lee; J.Y. Shin ๐Ÿ“‚ Article ๐Ÿ“… 2006 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 221 KB

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.

Hopscotch procedures for a fourth-order
โœ A. Danaee; D.J. Evans ๐Ÿ“‚ Article ๐Ÿ“… 1982 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 275 KB

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