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past_seminars/cam_colloquium/abstracts/CB0930.pdf(PDF). Mathematical notation is approximate — it comes from text extraction, not from the typeset source.
C. Bacutaa , J. Chenb , Y. Huangc , J. Xud , J. Suna and L. Zikatanovd a Department of Mathematical Sciences The University of Delaware b School of Mathematics and Computer Science Nanjing Normal University c Institute for Computational and Applied Mathematics Xiangtan University d Department of Mathematics The Pennsylvania State University
Work supported by UDRF and NSF
In this talk, we first give a general framework on applying the partition of unity method for nonmatching grids. Numerical aspects of discretization by partition of unity finite elements are considered for a model problem. We then present recent results on applying the method to Stokes equations discretized on nonmatching grids. The approach is based on creating global discrete spaces for velocity and pressure by gluing subspaces associated with subdomains. One main technical issue is the establishment of the Babuška-Brezzi’s in-sup condition for the new method.
References [1]I. Babuška and J. M. Melenk, ”The partition of unity finite element method: basic theory and applications.” Comput. Methods Appl. Mech. Engrg., 139, no. 1-4, 289 - 314, 1996. [2]Y. Huang, and J. Xu, ”A New Finite Element Method for Non-matching Grids Based on Partition of Unity”, Math. Comp. , v. 72, p. 1057-1066, 2002. [3] C. Bacuta, J. Chen, Y. Huang, J. Xu and L.T. Zikatanov, ”Partition of unity method on non-matching grids for the Stokes problem”, J. Chen, Y. Huang, J. Xu and L.T. Zikatanov, Journal of Numerical Mathematics, Vol.13, No.3, 2005, pp.157-236.