Thanks for your reply, sir. I'm new to FEM and for some concepts, I don't have clear understanding. I still have some problems： > Then you would want to compute the projection of d/dx u_h into this space via (phi_i, grad_x) = (phi_i, d/dx u_h) ------------------------------------- Is u_h means finite element method solution? If I'm right, how to understand `(phi_i, grad_x) = (phi_i, d/dx u_h)`? Why they are equal?[image: Snipaste_2021-05-22_09-30-16.png]
> This requires solving with a mass matrix, but at least the grad_x finite element function is a continuous function that you can then output ------------------------------------- What does 'mass matrix' mean here? 在2021年5月21日星期五 UTC+8 下午9:51:32<Wolfgang Bangerth> 写道： > On 5/20/21 8:49 AM, 沈键 wrote: > > Recently, I am writing codes to solve velocity potential equation which > is > > laplace equation form to solve the incompressible and inviscid airfoil > field. > > And after solving the system, I get the potential on each nodes. Then, I > use > > Datapostprocessor class to calculate solution's derivatives and output > to > > tecplot format. I find the solution is continous in tecplot, but its > > derivative is not. And I have learned that for Q1/Q2,etc element, its > > derivative is not continous between adjacent cells in theory, but in > > engineering we usually smooth the values between adjacent cells. My > question is: > > -*Is there any easy way to smooth the values between adjacent cells*？(I > > believe dealii has considered this problem, but I just didn't find any > > examples from tutorial.) > > No "easy" way with DataPostprocessor at least. What DataPostprocessor does > is > to faithfully output the gradient, which is indeed a discontinuous > function. > > The way to do this is to create a (continuous) finite element field onto > which > you project the gradient. For example, let's say you define an FE_Q (and > associated DoFHandler) for the x-derivative of your solution. Then you > would > want to compute the projection of d/dx u_h into this space via > > (phi_i, grad_x) = (phi_i, d/dx u_h) > > This requires solving with a mass matrix, but at least the grad_x finite > element function is a continuous function that you can then output. > > Best > W. > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: [email protected] > 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 --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/e52a9ec9-757e-4931-99d7-578717d58258n%40googlegroups.com.
