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What are the practical differences between a Galerkin finite element method vs an orthogonal collocation method? The best reference I've found thus far as been a paper titled The Performance of the Collocation and Galerkin Methods with Hermite Bi-Cubics by Dyksen, Houstis, Lynch, and Rice. To me, it seems like:

  • When comparable elements used, same asymptotic convergence rate
  • Assembly for collocation slightly easier since it can occur one row at a time (rows correspond to collocation points) rather than in Galerkin methods where an element stiffness or mass matrix is assembled and then summed into the global matrix
  • Bandwidth slightly lower on collocation, but a nonsymmetric system is generated even when the original problem is self-adjoint
  • Galerkin methods generate a symmetric system when the original operator is self-adjoint

Does this sound correct? Are there other practical differences such as preconditioner suitability, problems with ad-hoc methods like mass lumping, flexibility enforcing boundary conditions, or other intangibles that may favor one method over another given a certain situation?

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