On 7/23/20 12:07 PM, Xuefeng Li wrote:

Well, the above function calculates the gradients of a finite element at the quadrature points of a cell, not at the nodal points of a cell.
Such a need arises in the following situation.

for ( x in vector_of_nodal_points )
   v(x) = g(x, u(x), grad u(x))

It's worth pointing out, however, that for the common FE_Q elements, the function values u(x) are continuous and so it doesn't matter how exactly you compute u(x) at node points. On the other hand, grad u(x) is in general discontinuous and so trying to evaluate it at node points is not actually possible: You will either get the values from one adjacent cell or the value from another.

In other words, if you want to compute a function that depends on 'grad u', you need to think about what exactly you mean by that. In the formulation above, v(x) will in general be a discontinuous function, and you need to think about whether using FE_Q (a continuous finite element space) is really what you want to do.


Wolfgang Bangerth          email:                 bange...@colostate.edu
                           www: http://www.math.colostate.edu/~bangerth/

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