In this paper, we study the unconditional convergence and error estimates of a Galerkin-mixed FEM with the linearized semi-implicit Euler scheme for the equations of incompressible miscible flow in porous media. We prove that the optimal L2 error estimates hold without any time-step (convergence) conditions, while all previous works require certain time-step restrictions. Our theoretical result...

Least-squares finite element methods are motivated, beside others, by the fact that in contrast to standard mixed finite element methods, the choice of the finite element spaces is not subject to the LBB stability condition and the corresponding discrete linear system is symmetric and positive definite. We intend to benefit from these two positive attractive features, on one hand, to use differ...

In this paper, a comparison of weak-form Galerkin and least-squares finite element models of Timoshenko beam theory with the von Kármán strains is presented. Computational characteristics of the two models and the influence of the polynomial orders used on the relative accuracies of the two models are discussed. The degree of approximation functions used varied from linear to the 5th order. In ...

A two-grid scheme based on mixed finite-element approximations to the incompressible Navier-Stokes equations is introduced and analyzed. In the first level the standard mixed finite-element approximation over a coarse mesh is computed. In the second level the approximation is postprocessed by solving a discrete Oseen-type problem on a finer mesh. The two-level method is optimal in the sense tha...

Displacement finite element models of various beam theories have been developed using traditional finite element interpolations (i.e., Hermite cubic or equi-spaced Lagrange functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, total rotation φ and/or shear strain γxz, or in the integral form u...

This paper is about discrete sensitivity analysis. A triangular bending element with constant moment and six degrees of freedom is used. The required derivatives for sensitivity analysis are calculated explicitly. These formulations, finite element method and sequential linear programming are utilized to find shape optimization of plate bending structures. The numerical examples, which show the...

<p style='text-indent:20px;'>In this article, we develop a new mixed immersed finite element discretization for two-dimensional unsteady Stokes interface problems with unfitted meshes. The proposed IFE spaces use conforming linear elements one velocity component and non-conforming the other component. pressure is approximated by piecewise constant. Unisolvency, among fundamental propertie...