A mathematical model for the steady, mixed convection heat and mass transfer along a semi-infinite vertical plate embedded in a micropolar fluid in the presence of Soret and Dufour effects is presented. The non-linear governing equations and their associated boundary conditions are initially cast into dimensionless forms using local similarity transformations. The resulting system of equations is then solved numerically using the Keller-box method. The numerical results are compared and found to be in good agreement with previously published results as special cases of the present investigation. The non-dimensional velocity, microrotation, temperature and concentration profiles are displayed graphically for different values of coupling number, Soret and Dufour numbers. In addition, the skin-friction coefficient, the Nusselt number and Sherwood number are shown in a tabular form.

In this paper, we investigate the superconvergence results for optimal control problems governed by parabolic equations with semi-discrete mixed finite element approximation. We use the lowest order mixed finite element spaces to discrete the state and costate variables while use piecewise constant function to discrete the control variable. Superconvergence estimates for both the state variable and its gradient variable are obtained.

An axisymmetric formulation for modeling three-dimensional deformation of structures of revolution is presented. The axisymmetric deformation model is described using the cylindrical coordinate system. Large displacement effects and material nonlinearities and anisotropy are accommodated by the formulation. Mathematical derivation of the formulation is given, and an example is presented to demonstrate the capabilities and efficiency of the technique compared to the full three-dimensional model.

In this paper, we study the numerical solution of the Stokes system in deformed axisymmetric geometries. In the azimuthal direction the discretization is carried out by using truncated Fourier series, thus reducing the dimension of the problem. The resulting two-dimensional problems are discretized using the spectral element method which is based on the variational formulation in primitive variables. The meridian domain is subdivided into elements, in each of which the solution is approximated by truncated polynomial series. The results of numerical experiments for several geometries are presented.

The accuracy and efficiency of a class of finite volume methods are investigated for numerical solution of morphodynamic problems in one space dimension. The governing equations consist of two components, namely a hydraulic part described by the shallow water equations and a sediment part described by the Exner equation. Based on different formulations of the morphodynamic equations, we propose a family of three finite volume methods. The numerical fluxes are reconstructed using a modified Roe's scheme that incorporates, in its reconstruction, the sign of the Jacobian matrix in the morphodynamic system. A well-balanced discretization is used for the treatment of the source terms. The method is well-balanced, non-oscillatory and suitable for both slow and rapid interactions between hydraulic flow and sediment transport. The obtained results for several morphodynamic problems are considered to be representative, and might be helpful for a fair rating of finite volume solution schemes, particularly in long time computations.

In this paper, we study an adaptive finite element method for a class of nonlinear eigenvalue problems resulting from quantum physics that may have a nonconvex energy functional. We prove the convergence of adaptive finite element approximations and present several numerical examples of micro-structure of matter calculations that support our theory.