scalar interpolation inside Hex & Tet

Hi, I am trying to solve the following problem

I have a HEX8 (or TET4) element. I know the coordinates of its vertices. I also know the 8 (or 4 for TET) scalar values at each vertex. Now given a point inside this HEX8 (or TET4), I want to find out the interpolated scalar value at this location.

I tried using Barycentric Coordinates for interpolation. I also tried Shepard's Method for interpolation. But as my scalar data are cubic in nature, the error is huge(>40%). Basically this data can be anything (typically I will read a FEM solver output).

I would appreciate if you point me some document and/or code which is applied to the solution of the problem.

Thanks in advance

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The consistent approach is to use the element shape function.

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