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Consider a line element in FEM. Let each node have 3 DOF. They are x and y translation DOF and temperature. Can we use interpolation functions of different orders for the translation DOFs and Temperature, like say, first-order interpolation function for translation DOF and second-order interpolation for temperature?

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Yes, of course you can. You end up with something that is often called "mixed finite elements" if, for example, you are considering a formulation that involves velocities and pressures.

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  • $\begingroup$ Is it possible to have interpolation functions of a different order for the different components of velocity? $\endgroup$ – GRANZER Nov 4 '19 at 2:26
  • $\begingroup$ I suspect you could, but that seems strange to me. Why would you do that? I don't know anyone who has done that and can think of many reasons not to. $\endgroup$ – Wolfgang Bangerth Nov 4 '19 at 14:19

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