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How is the Petrov-Galerkin FEM different from more common FEMs? Could anyone give a layman description? What's the advantages of using the Petrov-Galerkin FEM?

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The difference between the Galerkin (=FEM) and Petrov-Galerkin methods is that in the former test and trial functions are the same, whereas in the latter they are not.

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  • $\begingroup$ thanks a lot. What's the advantages of using the Petrov-Galerkin FEM? $\endgroup$
    – feynman
    Feb 11 at 3:04
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    $\begingroup$ Well, I think that's debatable. There are certainly cases where it is useful, whereas in others one could ask why it was necessary to propose a method that uses Petrov-Galerkin approaches when there are already plenty of good methods around. I think the best example of the former would be Streamline Upwind Petrov-Galerkin (SUPG). You might want to read up on that. $\endgroup$ Feb 11 at 19:40
  • $\begingroup$ very helpful thanks. matlab has a pdepe solver solving parabolic and elliptic PDEs, which is based on Petrov-Galerkin. If SUPG is designed to solve convection dominated ones, why would matlab use this algorithm for solving non-hyperbolic ones? $\endgroup$
    – feynman
    Feb 12 at 3:56
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    $\begingroup$ I would have no idea! $\endgroup$ Feb 13 at 2:11

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