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
N_1,1(x,y)	N_1,2(x,y)	N_2,2(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.

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 U_t+U_xx+U_xy+U_yx=0	Solving the equation U_t+U_xx+U_xy+U_yx=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
Gravitation	Ecology	Electronics	PDEs	Other pages

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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