"Like Bruno already said in other words, you are starting at the wrong end 
of
the question. In a first step, define mathematically *what* it is you want 
to
do (and justify why this is the right choice). Then, in a second step, one 
can
think about *how* to implement this."

I need this function (triangulation) for post-processing, but also during 
my assemble routine.
Basically, the values of this function at some points are assembled into my 
linear system.
But it may happen that I have to evaluate the function at a point which is 
not contained in its triangulation,
since I do not know the bounds a priori. 
Currently, my program is aborted if I would need to evaluate at a point 
outside the triangulation. 
I want to circumvent this by extrapolating the function somehow (bilinear, 
...).
The function should be increasing in x-and y-direction and is quite smooth 
at the boundary.

Any suggestions?

Thank you,

Math

Wolfgang Bangerth schrieb am Mittwoch, 7. Juni 2023 um 16:33:32 UTC+2:

> On 6/6/23 14:24, Mathieu wrote:
> > 
> > for a post-processing step, I have to evaluate my temperature field at 
> some 
> > points outside the mesh close to its boundary.
> > 
> > I know that shape functions are not defined outside the mesh, that's why 
> I 
> > wanted to extrapolate them.
> > My idea was to use the gradient of the temperature field to come up with 
> an 
> > extrapolation.
> > But I do not know if that's reasonable.
>
> Like Bruno already said in other words, you are starting at the wrong end 
> of 
> the question. In a first step, define mathematically *what* it is you want 
> to 
> do (and justify why this is the right choice). Then, in a second step, one 
> can 
> think about *how* to implement this.
>
> Best
> W.
>
> -- 
> ------------------------------------------------------------------------
> Wolfgang Bangerth email: bang...@colostate.edu
> www: http://www.math.colostate.edu/~bangerth/
>
>
>

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