Finite element approximation plays an important role in the numerical methods of optimal control problems. There have been extensive theoretical and numerical studies for the finite element approximation of various optimal control problems. However the literature is too huge to even give a very brief review here. In recent years, the adaptive finite element method has been extensively investiga...

Reference [1] introduces a method for the computation of the Floquet matrix, which is a time-history solution of a periodic-coefficient system over one period. Reference [2] generalizes both first order and second order forms to the case for which all coefficients are periodic. Numerical results for rotor flap-lag response show the Sinha method to be much more efficient than conventional time-m...

The nonoverlapping domain decomposition methods form a class of domain decomposition methods, for which the information exchange between neighboring subdomains is limited to the variables directly associated with the interface, i.e. those common to more than one subregion. Our objective is to design algorithms in 3D for which we can find an upper bound on the condition number κ of the precondit...

for the nonlinear analysis of structures using the well known newton-raphson method, the tangent stiffness matrices of the elements must be constructed in each iteration. due to the high expense required to find the exact tangent stiffness matrices, researchers have developed novel innovations into the newton-raphson method to reduce the cost and time required by the analysis. in this paper, a ...

The hp version of the finite element method (hp-FEM) combined with adaptive mesh refinement is a particularly efficient method for solving partial differential equations because it can achieve a convergence rate that is exponential in the number of degrees of freedom. hp-FEM allows for refinement in both the element size, h, and the polynomial degree, p. Like adaptive refinement for the h versi...

this research work is devoted to the development of a mathematical model for the simulation of the flow of polymeric melts through the die region of extruders. a set of governing equations are solved using finite element method. standard galerkin technique is used in conjunction with the mixed scheme to solve the flow equation. due to the non-linear nature of global equations, the picard iterat...

In this paper, we present uniform convergence results for the mortar finite element method (which is an example of a non-conforming method), for h, p and hp discretizations over general meshes. Our numerical and theoretical results show that the mortar finite element method is a good candidate for hp implementation and also that the optimal rates afforded by the conforming h, p and hp discretiz...

Various methods for treating nonhomogeneous Dirichlet boundary conditions for the p-version of the finite element method are presented. These methods are theoretically and comrutationally analyzed. Numerical experimentations are given. They clearly illustrate the importance of the right treatment of the nonhomogeneous Dirichlet boundary conditions.

We investigate the use of numerical quadrature in the p-version of the finite element method. We describe a set of minimal conditions that the quadrature rules should satisfy, for various types of elements. Under sufficient assumptions of smoothness, we establish optimality of the asymptotic rate of convergence. Some computational results are presented, which illustrate under what conditions ov...