Defining Lagrange linear basis function (P1) on P2 isoparametric triangular element

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Is it correct to define Lagrange linear basis functions on p2 isoparametric triangular element.

We know the subparametric elememts whose shape functions are high order polynomials (n>=2), but the edges of the element are straight.

I wonder whether the 'inverse' definition is correct, more precisely:

Define low order polynomial basis functions on high order isoparametric elements.

I tried to solve Poisson equation on unit circle, and in order to approximate the curvilinear boundary, I wanted to use quadratic (cubic) isoparametric element with utmost one curvilinear edge (on the boundary).

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