I am working on a model in COMSOL and I am usin different meshes from coarse to fine keeping the other parameters constant. And, I got different maximum velocities for all the meshes.

What can I do to achieve similar maximum velocities for all the simulations?

  • $\begingroup$ Welcome to SciComp.SE. Can you provide more detail about your problem? Are you solving Navier-Stokes? $\endgroup$ – nicoguaro Mar 19 '16 at 15:29
  • $\begingroup$ Also, for the Finite Element Method you should not expect to obtain the same maximum speed for different meshes. Have you run a convergence analysis? $\endgroup$ – nicoguaro Mar 19 '16 at 15:30
  • $\begingroup$ Are they significantly different or are they converging towards a specific value? It is a natural consequence that increasing mesh resolutions leads to consequently better estimation of quantities. $\endgroup$ – nluigi Mar 20 '16 at 9:25

The finite element methods, i.e., what COMSOL uses internally, does not solve the problem exactly. It only (i) provides an approximation to the solution, and (ii) does so in a way for which we can show that the approximation converges to the exact solution of the problem as mesh becomes finer and finer. This typically implies that on meshes that are too coarse the difference between the approximation and the exact solution will be large.

Convergence, however, also implies that as you make your mesh finer and finer, the difference will become smaller and smaller. In other words, as long as you see significant differences between the solution on one mesh and the next, you can expect that both are inaccurate and unreliable. On the other hand, if you see no significant differences on two or more finer and finer meshes, you may hope that the approximation is reasonably close to the exact solution and can be trusted to a certain degree.


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