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 L2 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 elem...

We consider control-volume mixed finite element methods for the approximation of second-order elliptic problems on rectangular grids. These methods associate control volumes (covolumes) with the vector variable as well as the scalar, obtaining local algebraic representation of the vector equation (e.g., Darcy’s law) as well as the scalar equation (e.g., conservation of mass). We establish O(h2)...

In this paper, we discuss the a posteriori error estimates of the mixed finite element method for quadratic optimal control problems governed by linear parabolic equations. The state and the co-state are discretized by the high order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. We derive a posteriori error estimates for both the sta...

In this paper, we consider the error estimates of the numerical solutions of a class of fourth order linear-quadratic elliptic optimal control problems by using mixed finite element methods. The state and co-state are approximated by the order k Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise polynomials of order k (k ≥ 1). L and L-error estimate...

In this paper, we study the variational discretization and adaptive mixed finite element methods for optimal control problems governed by integro-differential equations. The state and the co-state are discretized by the lowest order Raviart-Thomas mixed finite element spaces and the control is not discretized. We derive a posteriori error estimates for the coupled state and control approximatio...

In this paper, we investigate the rectangular mixed finite element methods for the quadratic convex optimal control problem governed by nonlinear elliptic equations with pointwise control constraints. The state and the co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. We derive L∞-error estim...

We propose a 3D conforming-nonconforming mixed finite element for solving symmetric stress Stokes equations. The low-order conforming finite elements are not inf-sup stable. The low-order nonconforming finite elements do not satisfy the Korn inequality. The proposed finite element space consists of two conforming components and one nonconforming component. We prove that the discrete inf-sup con...

In this paper we analyze the finite element discretization for the first-order system least squares mixed model for the second-order elliptic problem by means of using nonconforming and conforming elements to approximate displacement and stress, respectively. Moreover, on arbitrary regular quadrilaterals, we propose new variants of both the rotated Q1 nonconforming element and the lowest-order ...

Mixed variational multiscale methods and multiscale finite elements