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<mailto:simulation...@gmail.com>> on behalf of Vikram Garg <vikram.v.g...@gmail.com<mailto:vikram.v.g...@gmail.com>> Date: Friday, September 9, 2016 at 2:13 PM To: Miguel Salazar <salazardet...@llnl.gov<mailto:salazardet...@llnl.gov>> Cc: "libmesh-users@lists.sourceforge.net<mailto:libmesh-users@lists.sourceforge.net>" <libmesh-users@lists.sourceforge.net<mailto: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<mailto: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<mailto:simulation...@gmail.com>> on behalf of Vikram Garg <vikram.v.g...@gmail.com<mailto:vikram.v.g...@gmail.com>> Date: Wednesday, September 7, 2016 at 10:00 AM To: Miguel Salazar <salazardet...@llnl.gov<mailto:salazardet...@llnl.gov>> Cc: "libmesh-users@lists.sourceforge.net<mailto:libmesh-users@lists.sourceforge.net>" <libmesh-users@lists.sourceforge.net<mailto:libmesh-users@lists.sourceforge.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<mailto: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<mailto:simulation...@gmail.com>> on behalf of Vikram Garg <vikram.v.g...@gmail.com<mailto:vikram.v.g...@gmail.com>> Date: Tuesday, September 6, 2016 at 7:19 PM To: Miguel Salazar <salazardet...@llnl.gov<mailto:salazardet...@llnl.gov>> Cc: "libmesh-users@lists.sourceforge.net<mailto:libmesh-users@lists.sourceforge.net>" <libmesh-users@lists.sourceforge.net<mailto:libmesh-users@lists.sourceforge.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<mailto: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-SummerSchool-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/weighted_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<mailto: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 ------------------------------------------------------------------------------ _______________________________________________ Libmesh-users mailing list Libmesh-users@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/libmesh-users
