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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
19910015503
Acquisition Source
Legacy CDMS
Document Type
Technical Memorandum (TM)
Authors
Jiang, Bo-Nan (NASA Lewis Research Center Cleveland, OH, United States)
Date Acquired
September 6, 2013
Publication Date
April 1, 1991
Subject Category
Numerical Analysis
Report/Patent Number
NASA-TM-103773
ICOMP-91-03
NAS 1.15:103773
E-6039
Accession Number
91N24817
Funding Number(s)
CONTRACT_GRANT: NASA ORDER C-99066-G
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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