Extrusion of aluminum sections is analyzed with a solution hp-adaptive finite element model. The analysis is based on the assumption that the elastic effects are negligible and rigid-viscoplastic material behavior is acceptable. The equations governing the flow of incompressible non-Newtonian fluids are solved using an iterative penalty finite element model. An error estimation scheme based on ...

Enriched finite element approaches such as the extended finite element method provide a framework for constructing approximations to solutions of non-smooth problems. Internal features, such as boundaries, are represented in such methods by using discontinuous enrichment of the standard finite element basis. Within such frameworks, however, imposition of interface constraints and/or constitutiv...

In this article we develop both the a priori and a posteriori error analysis of hp– version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain Ω ⊂ R, d = 2, 3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm which are explicit in the local ...

In this paper we investigate the performances of high-order of finite element methods for American option pricing. First of all, the partial differential problem that yields the price of American options, which is a free boundary problem, is transformed to a problem with a fixed boundary by adding a suitable penalty term. Then, by employing a quadratic finite element method, a nonlinear system ...

We investigate an a posteriori error analysis of adaptive finite element approximations of linear-quadratic boundary optimal control problems under bilateral bound constraints, which act on a Neumann boundary condition. We use a symmetric interior penalty Galerkin (SIPG) method as discretization method. An efficient and reliable residual-type error estimator is introduced by invoking data oscil...

This paper describes a finite element formulation designed to simulate polymer melt flows in which both conductive and convective heat transfer may be important, and illustrates the numerical model by means of computer experiments using extruder drag flow and entry flow as trial problems. Fluid incompressibility is enforced by a penalty treatment of the element pressures, and the thermal convec...

The aim of this paper is to develop and analyze a family of stabilized discontinuous finite volume element methods for the Stokes equations in two and three spatial dimensions. The proposed scheme is constructed using a baseline finite element approximation of velocity and pressure by discontinuous piecewise linear elements, where an interior penalty stabilization is applied. A priori error est...