๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Two bracketing theorems characterizing the eigensolution for the h-version of the finite element method

โœ Scribed by L. Meirovitch; L. M. Silverberg

Publisher
John Wiley and Sons
Year
1983
Tongue
English
Weight
655 KB
Volume
19
Category
Article
ISSN
0029-5981

No coin nor oath required. For personal study only.

โœฆ Synopsis

This paper demonstrates that the classical inclusion principle is in general not valid for the k-version of the finite element method. Whereas the inclusion principle is valid for second-order systems discretized by the h-version of the finite element method, provided linear interpolation functions are used as admissible functions, the principle is not valid for fourth-order systems. To characterize the computed eigenvalues for fourth-order systems discretized by the h-version of the finite element method, this paper formulates two bracketing theorems.

๐Ÿ“œ SIMILAR VOLUMES

The h-p version of the finite element me
The h-p version of the finite element method for parabolic equations. II. The h-p version in time
โœ Ivo Babuลก; Tadeusz Janik ๐Ÿ“‚ Article ๐Ÿ“… 1990 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 790 KB

## Abstract The paper is the second in the series addressing the __hโ€p__ version of the finite element method for parabolic equations. The present paper addresses the case when in both variables, the spatial and time, the __hโ€p__ version is used. Error estimation is given and numerical computations

Performance of the hโ€“p version of the fi
Performance of the hโ€“p version of the finite element method with various elements
โœ I. Babuลกka; H. C. Elman ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 928 KB

The paper addresses the performance of square elements of type Q ( p ) and Q'(p). ( Q ( p ) and Q ' ( p ) are elements of degree p, analogous to the well-known 9-and 8-noded elements for p = 2.) The performance is analysed theoretically for the class of analytic functions. Numerical experiments conf

The h-p version of the finite element me
The h-p version of the finite element method for parabolic equations. Part I. The p-version in time
โœ Ivo Babuska; Tadeusz Janik ๐Ÿ“‚ Article ๐Ÿ“… 1989 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 1000 KB

The paper is the first in the series addressing the h-p version of the finite element method for parabolic equations. The h-p version is applied to both time and space variables. The present paper addresses the case when in time the p-version with one single time element is used. Error estimation is