On 08/09/2017 03:46 PM, ky...@math.uh.edu wrote:

Hello all,I am working on implementing some stabilization methods for the Navier-Stokesequations, these techniques often require the use of the laplacian of theshape functions. I know I get the hessian of the k'th shape function atquadratue point q via the following| Tensor<3,dim>hessian_phi =fe_values[velocity_extractor].hessian(k,q); |My question is understanding what does this return, and how to extract thelaplacian from it. Does hessian_phi[ i ][ j ][ k ] = \frac{ \partial\varphi_{ i } } { \partial x_{ j } \partial x_{ k } }?

`I don't recall, but it should be documented somewhere with`

`FEValuesViews::Vector IIRC.`

If this is the case, is there a way to contract over the last two componentsto result in a rank 1 tensor that is the laplacian?

`Not as you are trying, but you can easily write the summation over the last`

`two indices by hand, of course.`

I've also seen that I can use shape_hessian_component since I am usingstandard Q2-Q1 elements,| intcomponent_i =fe.system_to_component(k ).first; Tensor<2,dim>hessian_phi =fe_values.shape_hessian_component(k,q,component_i ); |In this case I can get the laplacian of the i'th component of the k'th shapefunction at quadrature point q by trace( hessian_phi ). But this will resultin a rank 0 tensor.

Yes, it is the trace of the i'th component. You can then construct a Tensor<1,dim> traces; for (i=0...dim) { traces_phi = fe_values.shape_hessian_component (...); traces[i] = trace(hessian_phi) } Best W. -- ------------------------------------------------------------------------ Wolfgang Bangerth email: bange...@colostate.edu www: http://www.math.colostate.edu/~bangerth/ -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en

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