Graduate seminar SS 20 Graduate Seminar on Numerical Analysis
Adaptive Finite Element Methods
The seminar will take place as online-seminar (We 14-16):
- We will use the online meeting platform zoom. Applications can be downloaded for PC, Laptop, and mobile devices. Registration for the zoom platform is not necessary but free.
- The online presentations should be prepared using the latex beamer package to create a pdf file presentation. As for standard scientific talks at conferences, the beamer presentations will be scheduled for 30 minutes plus 15 minutes discussion.
- If under the new circumstances you still want to participate in the online seminar (and have chosen a topic already) please go ahead and register on basis.
- Once the eCampus system is ready, you will be assigned to an eCampus course automatically after registration in basis (note this might take some days since eCampus is currently busy creating all the courses)
- Further details on the online meetings will be displayed on eCampus by April 20th.
- If you want to participate in the seminar but have not yet chosen a topic please contact me via email.
- If you want to participate in the seminar and have chosen a topic but want to change to another topic please contact me via email.
- If under the new circumstances you do not want to participate and have chosen a topic please let me know via email so that somebody else might chose that topic.
- If you have not registered by the 20th in basis and want to take part in the first online meeting on April 22 please contact me via email for the meeting details on April 20th. (Those registered in basis will get the information on eCampus or via email to their uni email address)
- The talks will be scheduled during the first online meeting on April 22
The seminar is on adpative finite element methods.
The different topics have be discussed and assigned during the preliminary meeting on 27.01.2020 at 14:15 in room 2.035, EA19b. The schedule of the talks will be done during the first online meeting on 22.04.2020 at 14:15 on zoom.
Note that the following articles are only downloadable via the university library journal subscriptions, i.e. from any computer that is connected to the network of the University of Bonn, e.g. the computers of the library.
Literature (reserved for possible presentations during the preliminary meeting):
- Two Talks: Carstensen, C.; Feischl, M.; Page, M.; Praetorius, D.: Axioms of adaptivity. Comput. Math. Appl. 67 (2014), no. 6, 1195–1253
- Bonito, Andrea; Nochetto, Ricardo H.: Quasi-optimal convergence rate of an adaptive discontinuous Galerkin method. SIAM J. Numer. Anal. 48 (2010), no. 2, 734–771
- Braess, Dietrich: A posteriori error estimators for obstacle problems—another look. Numer. Math. 101 (2005), no. 3, 415–421
- Brenner, Susanne C.; Gudi, Thirupathi; Sung, Li-yeng: An a posteriori error estimator for a quadratic C^0-interior penalty method for the biharmonic problem. IMA J. Numer. Anal. 30 (2010), no. 3, 777–798
- Two Talks (part I on conforming): Ern, Alexandre; Vohralík, Martin: Polynomial-degree-robust a posteriori estimates in a unified setting for conforming, nonconforming, discontinuous Galerkin, and mixed discretizations. SIAM J. Numer. Anal. 53 (2015), no. 2, 1058–1081
- Carstensen, Carsten; Thiele, Jan: Partition of unity for localization in implicit a posteriori finite element error control for linear elasticity. Internat. J. Numer. Methods Engrg. 73 (2008), no. 1, 71–95
- Braess, Dietrich; Schöberl, Joachim Equilibrated residual error estimator for edge elements. Math. Comp. 77 (2008), no. 262, 651–672
- Carstensen, C.; Dolzmann, G.; Funken, S. A.; Helm, D. S.: Locking-free adaptive mixed finite element methods in linear elasticity. Comput. Methods Appl. Mech. Engrg. 190 (2000), no. 13-14, 1701–1718
- Stevenson, Rob: The completion of locally refined simplicial partitions created by bisection. Math. Comp. 77 (2008), no. 261, 227–241
- Diening, Lars; Kreuzer, Christian; Stevenson, Rob Instance optimality of the adaptive maximum strategy. Found. Comput. Math. 16 (2016), no. 1, 33–68
- Carstensen, Carsten; Gedicke, Joscha: An oscillation-free adaptive FEM for symmetric eigenvalue problems. Numer. Math. 118 (2011), no. 3, 401–427
- Carstensen, Carsten; Bartels, Sören: Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. I. Low order conforming, nonconforming, and mixed FEM. Math. Comp. 71 (2002), no. 239, 945–969
Literature (open for presentations):
- Two talks (part II on DG): Ern, Alexandre; Vohralík, Martin: Polynomial-degree-robust a posteriori estimates in a unified setting for conforming, nonconforming, discontinuous Galerkin, and mixed discretizations. SIAM J. Numer. Anal. 53 (2015), no. 2, 1058–1081
- Houston, Paul; Schötzau, Dominik; Wihler, Thomas P.: Energy norm a posteriori error estimation for mixed discontinuous Galerkin approximations of the Stokes problem. J. Sci. Comput. 22/23 (2005), 347–370
- Lederer, Philip Lukas; Merdon, Christian; Schöberl, Joachim: Refined a posteriori error estimation for classical and pressure-robust Stokes finite element methods. Numer. Math. 142 (2019), no. 3, 713–748
- Tobiska, L.; Verfürth: R. Robust a posteriori error estimates for stabilized finite element methods. IMA J. Numer. Anal. 35 (2015), no. 4, 1652–1671
- Huang, J., Huang, X., Xu, Y.: Convergence of an adaptive mixed finite element method for Kirchhoff plate bending problems. SIAM J. Numer. Anal. 49(2), 574–607 (2011)