Stationary Heat Conduction and Finite Elements

Stationary Heat Conduction is one of the simplest field problems, that can be investigated by Finite Elements.
It can be discribed by the Laplace Equation

λ(x,y) (∂²T/∂x² + ∂²T/∂y²) = 0.

That is a partial differential equation of second order. λ is the thermal conductivity. Unknown in this equation is the temperature T(x,y) over a 2-dimensional area.
For a complete formulation of the problem it is necessary to describe the boundary of the area and boundary conditions on that boundary.

The solution is found by means of Finite Elements. Here triangular elements with linear shape functions and isoparametic quadrangular elements are used.

 


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