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

DOI:
https://doi.org/10.1090/S0025-5718-99-01172-2

Published electronically:
August 24, 1999

MathSciNet review:
1665979

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 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

Email:
dpyang@math.sdu.edu.cn

DOI:
https://doi.org/10.1090/S0025-5718-99-01172-2

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