This paper deals with the convergence properties of the nonconforming quadrilateral Wilson element for a class of nonlinear parabolic problems in two space dimensions. Optimal H and L2 error estimates for the continuous time Galerkin approximations are derived. It is also shown for rectangular meshes that the gradient of the Wilson element solution possesses superconvergence, and that the Lx er...

This paper will describe recent work on the paving algorithm. The paving algorithm is an advancing front meshing method for generating quadrilateral elements on a general three dimensional surface. The work presented in this paper will describe the algorithmic changes to shift the paver from a row by row advancing front to an element by element method. This method modifies the paver to perform ...

This paper deals with the convergence properties of the nonconforming quadrilateral Wilson element for a class of nonlinear parabolic problems in two space dimensions. Optimal H and L2 error estimates for the continuous time Galerkin approximations are derived. It is also shown for rectangular meshes that the gradient of the Wilson element solution possesses superconvergence, and that the Lx er...

A new method with a simple algorithm was developed to accurately measure Poisson's ratio of soft materials such as polyvinyl alcohol hydrogel (PVA-H) with a custom experimental apparatus consisting of a tension device, a micro X-Y stage, an optical microscope, and a charge-coupled device camera. In the proposed method, the initial positions of the four vertices of an arbitrarily selected quadri...

The floor beams of steel buildings, cold-formed steel floor joists in particular, often require large web openings, which may affect their shear capacities. A cost effective way to mitigate the detrimental effects of such openings is to weld/fasten reinforcements. A difficulty associated with an experimental investigation to establish suitable reinforcement schemes for openings in shear zone is...

this study focuses on the optimization of the plane structure. sequential quadratic programming (sqp) will be utilized, which is one of the most efficient methods for solving nonlinearly constrained optimization problems. a new formulation for the second order sensitivity analysis of the two-dimensional finite element will be developed. all the second order required derivatives will be calculat...

In this part of the work, a notion of generalized enrichment is proposed to construct the global partition polynomials or to enrich global partition polynomial basis with extra terms corresponding to the higher order derivatives of primary variable. This is accomplished by either multiplying enrichment functions with the original global partition polynomials, or increasing the order of global p...

A recent study [4] reveals that convergence of finite element methods usingH(div ,Ω)compatible finite element spaces deteriorates on non-affine quadrilateral grids. This phenomena is particularly troublesome for the lowest-order Raviart-Thomas elements, because it implies loss of convergence in some norms for finite element solutions of mixed and least-squares methods. In this paper we propose ...