I got it. Thank your, sir! By the way, does deal.ii accept personal donation? I want to support this wonderful project. 在2021年5月24日星期一 UTC+8 下午11:37:36<Wolfgang Bangerth> 写道：
> On 5/21/21 7:37 PM, 沈键 wrote: > > 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? > > Yes, u_h is the solution for which you want to output the gradient. > > I should have chosen a different name than grad_x. I didn't mean this to > be > the gradient operator, but a function that corresponds to d/dx u_h. Let me > call this function gx, then you want to solve the problem > (phi_i, gx) = (phi_i, d/dx u_h) for all shape functions phi_i > and similarly if you want to output a continuous version of d/dy u_h, > you'd > solve for a function gy that satisfies > (phi_i, gy) = (phi_i, d/dy u_h) for all shape functions phi_i > > If you expand gx as > gx(x) = \sum_j GX_j phi_j(x) > then the problem you are trying to solve is > (phi_i, gx) > = \sum_j (phi_i,phi_j) GX_j > = (phi_i, d/dx u_h) > where M_ij = (phi_i,phi_j) is the mass matrix. > > 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/7201bb4e-3288-445f-a7f6-6779963cf4e3n%40googlegroups.com.
