[granzer]

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?

[granzer]

Can someone help me with this, please?

[FMDenaro]

Not an expert on FEM but I suppose that you have to consider if the fields are related each others or not. I mean, for example, if you use a second degree shape functions for the temperature, the heat flux should be described by a first degree shape function.
Pressure and velocity is a classical example where the shape function degree has to be congruent.
However, let we wait for answers by experts in FEM field.

[granzer]

Originally Posted by FMDenaro

Not an expert on FEM but I suppose that you have to consider if the fields are related each others or not. I mean, for example, if you use a second degree shape functions for the temperature, the heat flux should be described by a first degree shape function.
Pressure and velocity is a classical example where the shape function degree has to be congruent.
However, let we wait for answers by experts in FEM field.

Since heat flux is a gradient of temperature, it is understanding that it uses a hermitian interpolation. I am not sure.
Can you please tell me why you think the interpolation/shape functions of pressure and velocity be congruent? Also, can you tell me if the order of the interpolation functions for the different components of velocity can be different?

[praveen]

The answer will depend on the PDE you are solving. In some cases there are restrictions on what combination of approximation spaces will lead to a stable scheme.