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

Abstract

Abstract. Some least-squares mixed finite element methods for convectiondiffusion 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 leastsquares 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.

An optimal‐order error estimate on an H1‐Galerkin mixed method for a nonlinear parabolic equation in porous medium flow

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A mass-conservative characteristic splitting mixed element method for saltwater intrusion problem

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A Crank-Nicolson Characteristic Finite Element Method for Sobolev Equations

“…For the existence, uniqueness, and regularity of the solutions of the Sobolev equation (1.1), we refer to [3,4,20]. For Sobolev equations without a convection term, many mathematicians achieve the numerical results by classical finite element methods [1,6,10,11,12] or least-squares methods [9,15,16,21,22] or mixed finite element methods [8] or discontinuous finite element methods [13,14,18,19]. But in many situations, the convection term d (x ) · ∇u exists and d (x ) is large in order to describe a convection dominated diffusion.…”