# The Finite Element Method (II)

## The FEM in two dimensions

These are the shape functions for the 2-D quadrilateral finite element.

 N1,1(x,y) N1,2(x,y) N2,2(x,y)

## The weak formulation

The FE method is a numerical method to solve arbitrary PDEs. To achieve this objetive, it is a characteristic feature of the FE approach that the differential equations in question are first reformulated into an equivalent form, the so-called weak formulation. Thus, it is usual to talk about strong and weak forms. They are equivalent, but the weak form has some advantages:

• The approximating functions require to be differenciated less times than in the strong form.

• The weak formulation hold in an unchanged form even when discontinuities occur, whereas the presence of discontinuities requires a modification of the strong form.

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Last modified 4/2/2000 by Juan de Lara (Juan.Lara@ii.uam.es, http://www.ii.uam.es/~jlara) need help for using this courses?.

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