Numerical Integration
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To fix the most basic concepts on Numerical Integration, we will focus our description on a one dimensional integration using the Gauss-Legendre quadrature, that is, to solve: | To fix the most basic concepts on Numerical Integration, we will focus our description on a one dimensional integration using the Gauss-Legendre quadrature, that is, to solve: | ||
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== References == | == References == |
Revision as of 11:12, 3 November 2009
Numerical integration refers to all the procedures, algorithms and techniques in the numerical analysis to obtain an approximate solution to a definite integral.
That is, how to obtain a numerical value of:
where can be a 1D, 2D or 3D domain.
For our interest in the Finite Element Method, the purpose is to describe how the element matrices can be integrated numerically.
Gauss-Legendre Numerical Integration
To fix the most basic concepts on Numerical Integration, we will focus our description on a one dimensional integration using the Gauss-Legendre quadrature, that is, to solve:
References
- Carlos A. Felippa, "A compendium of FEM integration formulas for symbolic work", Engineering Computations, Vol. 21 No. 8, 2004, pp. 867-890, (c) Emerald Group Publishing Limited [1]
- Numerical Integration
- Gaussian Quadrature