Suppose we want to evaluate a function, derived through linear Lagrangian finite element, in a point which is not one of its nodes. Is a simple linear interpolation equal to the correct evaluation of the finite element function (i.e., a sum of weighted local tent function)?
2026-04-01 00:39:16.1775003956
Evaluation of a Function with Lagrangian Finite Element
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Yes. After all, that is what your FE model says.
However, this assumes that the node values that you interpolate from are results from the FEM computation. If instead you have the computed node values e. g. squared, then you should not interpolate the squared values, of course.
The story would also be different if you wanted to fit your degrees of freedom to some scattered data points. Reversing the interpolation is usually not optimal, and sometimes impossible (due to contradictions). But that is not the case here.