Finite Element Method (FEM)

Numerical integration (6)

In order to be able to apply the integration completely to Eq. 3-38, we need a transformation of the area expression dA of the global element that corresponds to the transformation that is used:

Eq. 3-38 can now be written as follows on the basis of the transformation:

The integrals in Eq. 3-45 that refer to the square master element can be calculated with the help of the Gauss quadrature method, so that the integral above can be calculated as follows for the two-dimensional case:

where K and N are the number of Gauss quadrature points,  are the Gauss coordinates, and Wi and Wj are the values of the weighting functions.

More detailed information about the application of the Gauss quadrature method can be found in [*1] among others.

 


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Module
Hydrodynamics of Floods
Source

TUHH

References

*1 Reddy (1993)

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