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

Yang, Dan-Ping

doi:10.1090/S0025-5718-99-01172-2

Analysis of least-squares mixed finite element methods for nonlinear nonstationary convection-diffusion problems
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Math. Comp. 69 (2000), 929-963 Request permission

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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