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This paper presents a superconvergence result of the stationary natural convection equations. The superconvergence result is obtained by applying a coarse mesh projection for finite element approximation. This projection method is actually a postprocessing procedure that constructs a new approximation based on a high order polynomial on coarse mesh, under some regularity assumption. Finally, numerical experiment is presented for testing, which confirms the theoretic analysis. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Several iterative schemes based on finite element discretization with triangulation for solving two-dimensional natural convection equations are studied in this article. We establish some reference points for evaluation of the possible impact from three kinds of schemes with respect to Rayleigh numbers. In case of [ABSTRACT FROM AUTHOR]

In this article, we present two-grid stable mixed finite element method for the 2D Burgers’ equation approximated by the-P1pair which satisfies the inf–sup condition. This method consists in dealing with the nonlinear system on a coarse mesh with widthHand the linear system on a fine mesh with widthh << Hby using Crank–Nicolson time-discretization scheme. Our results show that if we chooseH2=hthis method can achieve asymptotically optimal approximation. Error estimates are derived in detail. Finally, numerical experiments show the efficiency of our proposed method and justify the theoretical results. [ABSTRACT FROM PUBLISHER]

Three penalty finite element methods are designed to solve numerically the steady Navier-Stokes equations, where the Stokes, Newton, and Oseen iteration methods are used, respectively. Moreover, the stability analysis and error estimate for these nine algorithms are provided. Finally, the numerical tests confirm the theoretical results of the presented algorithms. Meanwhile, the numerical investigations are provided to show that the proposed methods are efficient for solving the steady Navier-Stokes equations with the different viscosity. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 74-94, 2014 [ABSTRACT FROM AUTHOR]

In this article, we consider the finite element method (FEM) for two-dimensional linear time-fractional Tricomi-type equations, which is obtained from the standard two-dimensional linear Tricomi-type equation by replacing the first-order time derivative with a fractional derivative (of order α, with 1 <α< 2 ). The method is based on finite element method for space and finite difference method for time. We prove that the method is unconditionally stable, and the error estimate is presented. The comparison of the FEM results with the exact solutions is made, and numerical experiments reveal that the FEM is very effective. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013 [ABSTRACT FROM AUTHOR]