Abstract
The last numerical method we will study is the so-called finite element method. Compared to the finite difference and finite volume method, the finite element method is the most stable numerical scheme which is why it is the most widely used method in computational fluid dynamics. For this method, the computational domain is first split up into small elements. For each element a so-called localized support function is constructed which is a function that is only defined within the respective element. The overall solution sought is obtained by “patching” together the individual solutions. We will illustrate this method using the velocity profile of the Hagen-Poiseuille flow.
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