The thing is though that I don't actually need to integrate at these 
points. The method still employ a 4node quad element in 2d or an 8 node hex 
element in 3d but only uses the element centroid to calculate the 
deformation gradient, no quadrature is actually done at that point so I 
feel like I need to interpolate otherwise the way deal makes the FESystem 
objects I'll now have quad points at all centroids that should be 
integrated, or am I misunderstanding something here?

On Thursday, December 22, 2016 at 9:21:01 AM UTC-5, Denis Davydov wrote:
>
> Hi
>
> On Thursday, December 22, 2016 at 5:47:24 AM UTC+1, [email protected] 
> wrote:
>>
>> I have gone through some of the tutorials previously and thought it was 
>> about time I actually tried to implement something on my own in the 
>> library. 
>>
>> I am attempting to implement a finite strain code using the F-Bar method. 
>> Essentially this is a single field formulation which requires the 
>> calculation the of the deformation gradient at the element center. The 
>> trick here is though that the element centroid isn't a vertex.
>>
>> My question is, is there a way to "interpolate" the displacement gradient 
>> at the element center without explicitly making it a quadrature point or 
>> will I have to implement my own quadrature formula for this method?
>>
>
> Yes, employ a custom quadrature formula with a single point with 
> coordinates {0.5, 0.5, 0.5} to feed it to FEValues. 
> There is no reason to figure out how to interpolate things, just use 
> Quadrautre<dim> and FEValues<dim> together to evaluate your solution at 
> quadrature point(s).
>
> Regards,
> Denis.
>  
>
>>
>> Thank you for any assistance that can be provided.
>>
>

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