Finite Element Method (FEM)

The weak form (4)

as well as the subsitution:

Eq. 3-12 can be transformed to:

where qn is the heat flux orthogonal to the boundary, which can also be written as:

The variables nx und ny are the components of the normal vector along the boundary.

The integral expression from Eq. 3-16 is called “weak form” of Eq. 3-7. The reader should now recall the first section of this chapter (… flipping pages back might be necessary). If we have a look at Eq. 3-16, we notice that the order of the differential referring to the variable T is not m=2 but m=1 in the integral (reduction), but at the same time a differential for  has been added (transport from T to ). Additionally, the natural boundary condition from Eq. 3-9 has been integrated into the weal form by means of the boundary integral.

 


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Hydrodynamics of Floods
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