> > Dear Prof. Bangerth, > Thanks for your quick reply!
> You mean you are wondering why the "grad u square" term grows with the size of the problem but "u square" does not? Yes, that's what I am confused. Our u_exact have exact "grad u_exact square" and "u_exact square". And our numerical solution "u" and its "grad u square" and "u square" should be approximation of the exact one though with adaptive mesh. So I think "grad u square" should not have so huge jump with different adaptive meshes, because they are all the approximation of "grad u_exact square". > I don't know either (and the one place I looked at in your code seems correct to me), but what happens if you do global refinement? Does it increase with a fixed ratio from one step to the next? I change the code in attaching, and the output is: Cycle 0: Number of active cells: 20 Number of degrees of freedom: 89 u square 0: 0.0305621 grad u square 0: 0.256542 Cycle 1: Number of active cells: 80 Number of degrees of freedom: 337 u square 1: 0.0489011 grad u square 1: 0.341164 Cycle 2: Number of active cells: 320 Number of degrees of freedom: 1313 u square 2: 0.0540201 grad u square 2: 0.361384 Cycle 3: Number of active cells: 1280 Number of degrees of freedom: 5185 u square 3: 0.0549874 grad u square 3: 0.365557 Cycle 4: Number of active cells: 5120 Number of degrees of freedom: 20609 u square 4: 0.0553762 grad u square 4: 0.367069 Cycle 5: Number of active cells: 20480 Number of degrees of freedom: 82177 u square 5: 0.0555421 grad u square 5: 0.367712 Cycle 6: Number of active cells: 81920 Number of degrees of freedom: 328193 u square 6: 0.0556186 grad u square 6: 0.367986 Cycle 7: Number of active cells: 327680 Number of degrees of freedom: 1311745 u square 7: 0.0556576 grad u square 7: 0.368119 and the ratio [image: ask-8-1.JPG] are: u_square: 1.8410 2.4038 1.3149 1.2287 1.1168 0.9720 grad_u_square: 2.0652 2.2766 1.4646 1.2336 1.2843 0.9891 And the results without adaptive mesh seem like approximate the exact results correctly. So I am confused why the results of "grad u square" with adaptive mesh are so strange? Maybe the reason is that we refinre mesh where the gradient of u is huge, so only "grad_u_square" can be very different with changing adaptive meshes? If so, how to deal with this problem? How to approximate "grad u_ecaxt square" correctly with changing adaptive mesh? Maybe change the value smaller of scale of refine cells and coarsen cells, to make the change smaller? Thank you very much! Best, Chucui -- 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]. For more options, visit https://groups.google.com/d/optout.
