Intro to FEA 4: Choosing Test Functions

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In order to get N equations and N unknowns, we need "N" trial functions to test the weak form of the equations. Here is the main way that is done (the fancy name is the Petrov-Galerkin scheme).
  1. Joseph Feser
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These videos are awesome. I keep coming back to the basics from time to time.

arashkhanegol
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The first part of the integral vanishes only at the boundary right? Becase w(x) will not be zero in the intermediary nodes, even if temperature at boundaries are known. Also, I am not able to mathematically grasp how w(x) = 0 if boundary temperatures are known. They should be 0 even if the boundary temperatures are unkown, cz them being 0 is because of all the tent functions being 0 at the boundary.

kumarsatyam