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.
Best
W.
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