Yes, actually both schemes converge to the same solution. Maybe I should do some postprocessing with a visualiuation in order to figure out what the lumped integration does with the values at the qps.
I´ve got one more basic question ragarding the determination of the convergence rate as it is done in many tutorials (step 7, step 51,...). For that purpose I watched your new videos (3.9, 3.91, 3.93, 3.95) where you derived the error estimation for the laplace equation in certain norms. You mentioned in there that for many PDEs one comes up with the same results, i.e. that the finite element error is at least as good as the interpolation error *times some equation-dependent constant*. I want to determine the convergence rate for the elasticity equations with the PDE: div(stress-tensor) = 0. -Since I determine the convergence rate, the before mentioned *constant* in the inequality cancels out, i.e. I should get the same convergence rate as for the laplace equation. Is that right? -I actually solve the nonlinear elasticity equations (hyperelasticity); The finite element spaces, test functions,... are the same as for linear elasticity, but the stresses depend now nonlinear on the gradient of the displacements. My question is if the nonlinearity changes the error estimates? Let´s assume I determine the convergence rate in the L2-norm for linear elasticity, which is in the best case 2 for for p=1. Should I also get 2 for the nonlinear elasticity equations? I know that these questions are not directly related to dealii, but I guess you have a deep knowledge in that area. I would appreciate if you helped my answering that. Best Simon Wolfgang Bangerth schrieb am Sonntag, 6. Juni 2021 um 01:58:39 UTC+2: > On 6/4/21 9:14 AM, Simon Wiesheier wrote: > > > > So intuitively speaking, what is the effect of the lumped integration? > From a > > mathematical viewpoint there are no more couplings between the DoFs. But > does > > this lead to lower nodal values, higher nodal values or is this context > dependent? > > I have to admit that I have no intuition. > > Do both schemes converge? To the same solution? > > Best > W. > > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: bang...@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 --- 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 dealii+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/30a00e59-625d-403e-812f-cc051802deeen%40googlegroups.com.
