If you are referring to equation 3.30, yes this should be a good estimator for the L2 error once the constant C has been obtained. The duality trick (Aubin-Nitsche) gives us the extra powers of h, which we expect to see in the L2 convergence.
On Fri, Sep 9, 2016 at 5:44 PM, Salazar De Troya, Miguel < salazardet...@llnl.gov> wrote: > I found an error estimator in the L2 norm here: https://www.ices.utexas. > edu/sites/oden/wp-content/uploads/2013/06/1997-006.a_posteriori.pdf , Pag > 23. Is this a good error estimator to use or is it the forward euler of the > error indicators? > > Thanks > > From: <simulation...@gmail.com> on behalf of Vikram Garg < > vikram.v.g...@gmail.com> > Date: Friday, September 9, 2016 at 2:13 PM > > To: Miguel Salazar <salazardet...@llnl.gov> > Cc: "libmesh-users@lists.sourceforge.net" <libmesh-users@lists. > sourceforge.net> > Subject: Re: [Libmesh-users] Dual weighted residual error estimator in > libMesh > > Hello Salazar, > > On Fri, Sep 9, 2016 at 1:49 PM, Salazar De Troya, Miguel < > salazardet...@llnl.gov> wrote: > >> My problem with patch recovery is that it cannot be used across an >> interface where the gradient is discontinuous. >> > > I would say that even in cases where the gradient is discontinuous, patch > recovery will be ok to use as an error indicator, although definitely not > as an estimator. People have used the patch recovery for L2 error in a > problem with a shock (again a gradient discontinuity) and gotten good error > indicators. > > >> I also see that one has to be careful when using other error indicators >> because they might be designed for the error in the energy norm or the >> complete H1 norm, whereas your weighting approach needs error estimators >> separated for different cases (L2, H1 seminar, Hdiv seminorm) etc. >> > > Yes, this is why the approach works well the patch, which can give > separate estimates for the different variables and norms. Note that the > Kelly implementation in libMesh only computes derivative jumps, and not > flux jumps. > > Using complete H1 norm indicators in conjunction with adjoint residual > error indicators will make it difficult to apply the constitutive tensor, > since it acts on individual components of the solution/gradient. > > >> >> Miguel >> From: <simulation...@gmail.com> on behalf of Vikram Garg < >> vikram.v.g...@gmail.com> >> Date: Wednesday, September 7, 2016 at 10:00 AM >> >> To: Miguel Salazar <salazardet...@llnl.gov> >> Cc: "libmesh-users@lists.sourceforge.net" <libmesh-users@lists.sourcefor >> ge.net> >> Subject: Re: [Libmesh-users] Dual weighted residual error estimator in >> libMesh >> >> On Wed, Sep 7, 2016 at 11:54 AM, Salazar De Troya, Miguel < >> salazardet...@llnl.gov> wrote: >> >>> In the case I used the Adjoint Residual Error Estimator as an error >>> indicator to adaptively refine my mesh, will I obtain a more accurate goal >>> functional with less refinement than if I used a primal solution based >>> error indicator? Even if the error estimate of the goal functional is not >>> reliable. >>> >>> >> Yes, one would expect to achieve a better estimate of the goal functional >> (QoI) with the Adjoint Residual Estimator. The reliability of the error >> indicator depends on the estimators you use for the primal and dual weight >> calculations. Patch recovery tends to work well, and there is some theory >> behind this, which I can point to if there is interest. >> >> >>> With regards to the weighted error estimator, the implementation is for >>> the patch based recovery estimators, could I do something similar for other >>> error estimators, for instance, the Kelly error? >>> >> >> I believe extending the weighted indicator support to the Kelly error >> estimator should not be a problem. All the weights really do is scale >> contributions from each individual error component. >> >> >>> >>> Thanks >>> Miguel >>> From: <simulation...@gmail.com> on behalf of Vikram Garg < >>> vikram.v.g...@gmail.com> >>> Date: Tuesday, September 6, 2016 at 7:19 PM >>> To: Miguel Salazar <salazardet...@llnl.gov> >>> Cc: "libmesh-users@lists.sourceforge.net" <libmesh-users@lists.sourcefor >>> ge.net> >>> Subject: Re: [Libmesh-users] Dual weighted residual error estimator in >>> libMesh >>> >>> Hello Salazar, >>> >>> On Tue, Sep 6, 2016 at 5:46 PM, Salazar De Troya, Miguel < >>> salazardet...@llnl.gov> wrote: >>> >>>> Hello >>>> >>>> I started learning about the dual weighted residual error estimator. >>>> From what I read here: http://cadmus.usc.edu/UQ-Summe >>>> rSchool-2013/bauman.pdf there are two approaches in libMesh: One, >>>> calculate the adjoint solution in an enriched space; two, use a classic >>>> error estimator for both the primal and the adjoint solutions. I have two >>>> questions with regards to this approach: >>>> >>>> * What is the error incurred by choosing the second option? >>>> >>> >>> The second option (called Adjoint Residual Error Estimator) is suitable >>> for use as an *error indicator*, i.e. the calculation of an element wise >>> metric to decide whether they should be refined. For obtaining >>> reliable error estimates, the first option (Adjoint Refinement Estimator) >>> is the way to go. >>> >>> A combined strategy can also be used, where one does a few mesh >>> refinement steps using the Adjoint Residual approach, and then does a step >>> with the Adjoint Refinement Estimator to check whether error tolerances >>> have been met. >>> >>> >>>> * In the case of elasticity, how do we apply the constitutive >>>> tensor? In both error estimators or just the primal? Basically, in the >>>> above presentation, slide 66, the application of R_k >>>> >>> >>> If you use the Adjoint Refinement Error Estimator, the constitutive >>> tensor is automatically included via the definition of the residual one >>> provides in element_time_deriative. >>> >>> If you use the Adjoint Residual Indicator, and wish to include the >>> effect of the constitutive tensor, you will need to build a weights matrix. >>> See *Adjoints example 3*. >>> >>> If your constitutive tensor is nonlinear, then you will need to use the >>> weighted patch recovery estimator (see src/error_estimation/weig >>> hted_patch_recovery_estimator.C), specify the weight functions and >>> provide function pointers to them. *Adjoints example 3* covers this as >>> well. >>> >>> >>>> >>>> Thanks >>>> Miguel >>>> >>>> ------------------------------------------------------------ >>>> ------------------ >>>> _______________________________________________ >>>> Libmesh-users mailing list >>>> Libmesh-users@lists.sourceforge.net >>>> https://lists.sourceforge.net/lists/listinfo/libmesh-users >>>> >>> >>> Thanks. >>> -- >>> Vikram Garg >>> Postdoctoral Associate >>> The University of Texas at Austin >>> >>> http://vikramvgarg.wordpress.com/ >>> http://www.runforindia.org/runners/vikramg >>> >> >> >> >> -- >> Vikram Garg >> Postdoctoral Associate >> The University of Texas at Austin >> >> http://vikramvgarg.wordpress.com/ >> http://www.runforindia.org/runners/vikramg >> > > > > -- > Vikram Garg > Postdoctoral Associate > The University of Texas at Austin > > http://vikramvgarg.wordpress.com/ > http://www.runforindia.org/runners/vikramg > -- Vikram Garg Postdoctoral Associate The University of Texas at Austin http://vikramvgarg.wordpress.com/ http://www.runforindia.org/runners/vikramg ------------------------------------------------------------------------------ _______________________________________________ Libmesh-users mailing list Libmesh-users@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/libmesh-users
