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Analysis of least-squares mixed finite element methods for nonlinear nonstationary convection-diffusion problems

Author: Dan-Ping Yang
Journal: Math. Comp. 69 (2000), 929-963
MSC (1991): Primary 65N30, 35F15
Published electronically: August 24, 1999
MathSciNet review: 1665979
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Abstract: Some least-squares mixed finite element methods for convection-diffusion problems, steady or nonstationary, are formulated, and convergence of these schemes is analyzed. The main results are that a new optimal a priori $L^2$ error estimate of a least-squares mixed finite element method for a steady convection-diffusion problem is developed and that four fully-discrete least-squares mixed finite element schemes for an initial-boundary value problem of a nonlinear nonstationary convection-diffusion equation are formulated. Also, some systematic theories on convergence of these schemes are established.

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Additional Information

Dan-Ping Yang
Affiliation: Department of Mathematics, University of Shandong, Jinan, Shandong, 250100, P. R. China

Keywords: Least-squares algorithm, mixed finite element, nonlinear convection-diffusion problem, convergence analysis
Received by editor(s): January 2, 1998
Received by editor(s) in revised form: August 14, 1998
Published electronically: August 24, 1999
Additional Notes: The research was supported by the China State Major Key Project for Basic Researches and by the Doctoral Point Foundation and the Trans-Century Training Programme Foundation for Talents by the China State Education Commission.
Article copyright: © Copyright 2000 American Mathematical Society