%0 Journal Article %1 citeulike:13663597 %A Klawonn, Axel %A Starke, Gerhard %B Numerische Mathematik %D 1999 %I Springer-Verlag %K 76m10-finite-element-methods-in-fluid-mechanics 65f08-preconditioners-for-iterative-methods 65f10-iterative-methods-for-linear-systems 76d07-stokes-and-related-oseen-etc-flows %N 4 %P 577--594 %R 10.1007/s002110050405 %T Block Triangular Preconditioners for Nonsymmetric Saddle Point Problems: Field-of-Values Analysis %U http://dx.doi.org/10.1007/s002110050405 %V 81 %X A preconditioned minimal residual method for nonsymmetric saddle point problems is analyzed. The proposed preconditioner is of block triangular form. The aim of this article is to show that a rigorous convergence analysis can be performed by using the field of values of the preconditioned linear system. As an example, a saddle point problem obtained from a mixed finite element discretization of the Oseen equations is considered. The convergence estimates obtained by using a field–of–values analysis are independent of the discretization parameter h. Several computational experiments supplement the theoretical results and illustrate the performance of the method.

@article{citeulike:13663597, abstract = {{A preconditioned minimal residual method for nonsymmetric saddle point problems is analyzed. The proposed preconditioner is of block triangular form. The aim of this article is to show that a rigorous convergence analysis can be performed by using the field of values of the preconditioned linear system. As an example, a saddle point problem obtained from a mixed finite element discretization of the Oseen equations is considered. The convergence estimates obtained by using a field–of–values analysis are independent of the discretization parameter h. Several computational experiments supplement the theoretical results and illustrate the performance of the method.}}, added-at = {2017-06-29T07:13:07.000+0200}, author = {Klawonn, Axel and Starke, Gerhard}, biburl = {https://www.bibsonomy.org/bibtex/21a843be9a7ea2137089b6af3d2bcdbfb/gdmcbain}, booktitle = {Numerische Mathematik}, citeulike-article-id = {13663597}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/s002110050405}, citeulike-linkout-1 = {http://link.springer.com/article/10.1007/s002110050405}, doi = {10.1007/s002110050405}, interhash = {4de36f02272fdda9415e1643371084f8}, intrahash = {1a843be9a7ea2137089b6af3d2bcdbfb}, keywords = {76m10-finite-element-methods-in-fluid-mechanics 65f08-preconditioners-for-iterative-methods 65f10-iterative-methods-for-linear-systems 76d07-stokes-and-related-oseen-etc-flows}, number = 4, pages = {577--594}, posted-at = {2015-07-03 04:52:51}, priority = {2}, publisher = {Springer-Verlag}, timestamp = {2019-02-28T23:44:48.000+0100}, title = {{Block Triangular Preconditioners for Nonsymmetric Saddle Point Problems: Field-of-Values Analysis}}, url = {http://dx.doi.org/10.1007/s002110050405}, volume = 81, year = 1999 }