The Finite Element Method (II)

The FEM in two dimensions

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




2-D Linear and Quadratic Shape Functions for the Q4

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:

Theory pages:
Main page
FEM (i)
FEM (ii)
FDM (i)
Example pages:
1-d Heat Equation
2-d steady state Heat Equation
2-d Heat Equation
1-d non diffusive transport equation
1-d diffusive transport equation
2-d Non diffusive transport equation
Mesh generation with OOCSMP
Moving grids
Application pages:
Heating of two beams
Heating of two moving beams
Solving the equation Ut+Uxx+Uxy+Uyx=0
Solving the equation Ut+Uxx+Uxy+Uyx=0 using MGEN
Heat 1d using several outputs
Solving the Heat equation with a CA
Comparing a CA with the FEM
Gordon's sine equation

Other courses
Other pages

Last modified 4/2/2000 by Juan de Lara (, need help for using this courses?.

The SODA code