Hello together, I have the following problem: in my code, I would like to compute the Laplacian of some function, which is an element of V_vec = VectorFunctionSpace(mesh, "Lagrange", 1) I can use div(grad(U)) but the problem is, since the degree of the function space is 1, the laplacian is compu…

That would not work, as a projection into a higher dimensional space (that contains the linear polynomials), will still render you with a linear solution, and then the double derivative will be zero.

Would it be possible to define V_vec = VectorFunctionSpace(mesh, "Lagrange", 2) and then set U to be an element of V_vec. Then to project the laplacian of U to a lower dimensional function space?

That should in theory work, as grad(U) would be in "DG" 1, and div(grad(u)) in “DG” 0. I wouldn’t project this into “CG”, 1 as that is not a compatible finite element space.

Compute the Laplacian of trial functions

mathematics

dokken April 12, 2023, 12:01pm 3

See: Computing element-wise spatial derivatives of the solution - #4 by dokken

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Compute the Laplacian of trial functions

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