The combined effect of numerical integration and approximation of the boundary in the finite element method for eigenvalue problems

1995 ◽  
Vol 71 (2) ◽  
pp. 253-273 ◽  
Author(s):  
Michèle Vanmaele ◽  
Alexander Ženíšek
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Integration ◽  
Eigenvalue Problems ◽  
Combined Effect ◽  
The Finite Element Method ◽  
Effect Of Numerical Integration ◽  
Element Method

The Finite-Element Method—Part II

1989 ◽  
Author(s):  
Shiro Kobayashi ◽  
Soo-Ik Oh ◽  
Taylan Altan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Integration ◽  
Gaussian Quadrature ◽  
The Finite Element Method ◽  
Gaussian Quadrature Formula ◽  
Stiffness Matrices ◽  
Minimum Number ◽  
Element Technique ◽  
Element Method

Numerical integration is an important part of the finite-element technique. As seen in Section 6.5 of Chap. 6, volume integrations as well as surface integrations should be carried out in order to represent the elemental stiffness equations in a simple matrix form. In deriving the variational principle, it is implicitly assumed that these integrations are exact. However, exact integrations of the terms included in the element matrices are not always possible. In the finite-element method, further approximations are made in the procedure for integration, which is summarized in this section. Numerical integration requires, in general, that the integrand be evaluated at a finite number of points, called Integration points, within the integration limits. The number of integration points can be reduced, while achieving the same degree of accuracy, by determining the locations of integration points selectively. In evaluating integration in the stiffness matrices, it is necessary to use an integration formula that requires the least number of integrand evaluations. Since the Gaussian quadrature is known to require the minimum number of integration points, we use the Gaussian quadrature formula almost exclusively to carry out the numerical integrations.

Numerical Integration over Pyramids

2013 ◽  
Vol 5 (03) ◽  
pp. 309-320 ◽  
Author(s):  
Chuanmiao Chen ◽  
Michal Křížek ◽  
Liping Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Integration ◽  
Higher Order ◽  
The Finite Element Method ◽  
Hexahedral Elements ◽  
Cubature Formulae ◽  
Element Method

AbstractPyramidal elements are often used to connect tetrahedral and hexahedral elements in the finite element method. In this paper we derive three new higher order numerical cubature formulae for pyramidal elements.

A novel approach to suppress the DC modes in eigenvalue problems using the finite element method

2012 ◽  
Vol 55 (1) ◽  
pp. 210-212
Author(s):  
Marcos S. Gonçalves ◽  
Francisco J. Arnold ◽  
Leonardo L. Bravo-Roger ◽  
Talia S. Santos
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Eigenvalue Problems ◽  
The Finite Element Method ◽  
Novel Approach ◽  
Element Method
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