Hello, professor Wolfgang Thank you very much for your reply and it really helps me. You explained how to deal with the latter case (V'(u) . grad u, phi_i) and I've got the point how to solve this. Addtionally. how about the former case -(V(u), grad phi_i). Specifically, how to construct the vector V(u) and then multiply with grad phi_i or to say fe_values.shape_grad(i,q_point)?
Thank you very much! Best, Toddy 在2021年9月16日星期四 UTC+8 上午11:45:40<Wolfgang Bangerth> 写道： > On 9/15/21 6:33 AM, Toddy Liu wrote: > > > > I'm getting trouble in developing new code based on step-25. In step-25, > the > > equation to be solved is u_tt−∆u=−sin(u) and the tutorial shows me how > to > > solve such a nonlinear problem. > > > > Specifically, the tutorial tells me how to calculate (sin(u),φ_j)_Ω in > detail. > > So I 'm wondering how to solve such a problem which is like u_tt−∆u=∇∙V, > where > > V is a vector and its components(x direction and y direction in 2D) are > > dependent on u. So could you please give me some advice about doing this > or > > any reference in existing dealii examples. > > The standard point of departure is always the weak formulation of the > problem. > In your case, you will have a right hand side of the following form: > > (div V(u), phi_i) > > for which you can decide whether you want to integrate it by parts to get > > -(V(u), grad phi_i) + boundary terms > > or whether you want to leave it as is. If the latter, then you have to > apply > the chain rule and get something along the lines of > > (V'(u) . grad u, phi_i) > > which you have to deal with in much the same way as if you just had > > (sin(u), phi_i) > > except that you also have terms that involve derivatives of u. > > Does that make sense? > > 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/e3ea5c84-8bfc-4133-9989-136fdcba6e2dn%40googlegroups.com.
