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Can we use interpolation function of different order to represent different degrees o

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Old   November 3, 2019, 00:56
Default Can we use interpolation function of different order to represent different degrees o
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Mandeep Shetty
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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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Old   November 3, 2019, 22:30
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Can someone help me with this, please?
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Old   November 4, 2019, 03:35
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Filippo Maria Denaro
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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.
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Old   November 4, 2019, 03:53
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Quote:
Originally Posted by FMDenaro View Post
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?
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Old   November 5, 2019, 01:06
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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.
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