On Fri, Jul 24, 2020 at 9:58 PM Wolfgang Bangerth <bange...@colostate.edu>
wrote:
> 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.
>
> Indeed, grad u would be discontinuous under normal conditions when u is
approximated by FE_Q. I remember vaguely that such an issue was discussed
in one or more of the tutorial Step examples. Thanks for your follow-up.
--
Stay put, practice social distancing, and be safe!
Best,
--Xuefeng Li, (504)865-3340(phone)
Like floating clouds, the heart rests easy
Like flowing water, the spirit stays free
Loyola University New Orleans
New Orleans, Louisiana (504)865-2051(fax)
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