Question about fe_value.divergence

[yuesu jin]

Dear all,

  I am working on vector value finite element modeling. I read the pages  https://www.dealii.org/current/doxygen/deal.II/group__vector__valued.html which uses the fe_values.divergence and fe_value.grad, but I cannot find these two member functions in the FEValues\FESystem\FEValueBase categories. Could you give me the documentation page about these two functions?

Best regards,

--

Yuesu Jin,

Ph.D student,

University of Houston,

College of Natural Sciences and Mathematics,

Department of Earth and Atmospheric Sciences,
Houston, Texas 77204-5008


346-404-2062

[Wolfgang Bangerth]

On 9/3/20 1:28 PM, yuesu jin wrote:
>   I am working on vector value finite element modeling. I read the pages
> https://www.dealii.org/current/doxygen/deal.II/group__vector__valued.html

> <https://nam01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.dealii.org%2Fcurrent%2Fdoxygen%2Fdeal.II%2Fgroup__vector__valued.html&data=02%7C01%7CWolfgang.Bangerth%40colostate.edu%7Cb30f39009c8c49c8fc8108d8503f8631%7Cafb58802ff7a4bb1ab21367ff2ecfc8b%7C0%7C0%7C637347581059635256&sdata=w%2BABjRZ1fzUdFfCQvw49JwLF7Inl3iEG4XR78VwlgoA%3D&reserved=0> which

> uses the fe_values.divergence and fe_value.grad, but I cannot find these two
> member functions in the FEValues\FESystem\FEValueBase categories. Could you
> give me the documentation page about these two functions?

These functions only exist in FEValuesViews::Vector and FEValuesViews::Tensor.
You get that if you have something like

FEValuesExtractors::Vector velocities(0);
fe_values[velocities].divergence (...);

step-22 shows how this works in practice.

Best
W.

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

[yuesu jin]

Dear Dr. Bangerth,

  Thank you very much! I was confused about the shape function in the vector case.

  In step.8 we use the FEValue::shape_grad(index of shape function,index of quadrature point) and get a vector as the gradient of shape function. However, in step.20 and step.22, when we take the gradient of FESystem[vector_indices]::gradient(index of shape function, index of quadrature point) we get a rank-2 tensor. If the shape function is a vector, FEValue::shape_grad(index of shape function,index of quadrature point) should give a tensor as well. Does it mean that the shape_grad gives the gradient of the non-zero component in the vector shape function such that it is a vector?   

  Thank you again!

Best regards,

--
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[yuesu jin]

Dear Dr. Bangerth,

  I read the step.20 again. It solves my question. I didn't understand what the non-primitive element talks about, now I know the necessity of that. Thank you!

Best regards,

Yuesu

 

[Wolfgang Bangerth]

On 9/3/20 4:50 PM, yuesu jin wrote:
>   I read the step.20 again. It solves my question. I didn't understand what
> the non-primitive element talks about, now I know the necessity of that. Thank
> you!

Glad to hear!