The L sub 1 finite element method for pure convection problemsThe least squares (L sub 2) finite element method is introduced for 2-D steady state pure convection problems with smooth solutions. It is proven that the L sub 2 method has the same stability estimate as the original equation, i.e., the L sub 2 method has better control of the streamline derivative. Numerical convergence rates are given to show that the L sub 2 method is almost optimal. This L sub 2 method was then used as a framework to develop an iteratively reweighted L sub 2 finite element method to obtain a least absolute residual (L sub 1) solution for problems with discontinuous solutions. This L sub 1 finite element method produces a nonoscillatory, nondiffusive and highly accurate numerical solution that has a sharp discontinuity in one element on both coarse and fine meshes. A robust reweighting strategy was also devised to obtain the L sub 1 solution in a few iterations. A number of examples solved by using triangle and bilinear elements are presented.
Document ID
19930050329
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Jiang, Bo-Nan (Computational Physics System Ann Arbor, MI, United States)
Date Acquired
August 16, 2013
Publication Date
January 1, 1991
Publication Information
Publication: In: Numerical methods in laminar and turbulent flow; Proceedings of the 7th International Conference, Stanford Univ., CA, July 15-19, 1991. Vol. 7, pt. 1 (A93-34301 13-34)
Publisher: Pineridge Press
Subject Category
Fluid Mechanics And Heat Transfer
Accession Number
93A34326
Distribution Limits
Public
Copyright
Other
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IDRelationTitle19930050304Collected WorksNumerical methods in laminar and turbulent flow; Proceedings of the 7th International Conference, Stanford Univ., CA, July 15-19, 1991. Vol. 7, pts. 1 & 2