Method of weighted residuals -> Finite element form (2)

Eq. 3-1 to 3-4 are strictly speaking not a finite element formulation. Eq. 3-1 has to be modified first:

with:

u^{e}(x,y)

=

is an approximation of the solution u(x,y) over the element e

n

=

is the number of vertexes for the element e with the area

u_{j}^{e}

=

is the value of the function of u^{e}(x,y) at the vertex j of the element e

=

is the approximation- or weighting function for the element e

Note that the definition has already been made in Eq. 3-5 according to the Galerkin method.

If Eq. 3-5 is substituted into 3-4, we obtain the following general expression for the finite element form according to the method of weighted residuals: