We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of KohnSham density-functional theory (DFT). To this end, we develop an a priori mesh adaption technique to construct a close to optimal finite-element discretization of the problem. We further propose an efficient solution strategy ...

A standard finite element method and a finite element truncation method are applied to solve the boundary value problems of nonlinear elasticity with certain nonconvex stored energy functions such as those of St. Venant-Kirchhoff materials. Finite element solutions are proved to exist and to be in the form of minimizers in appropriate sets of admissible finite element functions for both methods...

The Moving Finite Element method for the solution of time-dependent partial dierential equations is a numerical solution scheme which allows the automatic adaption of the nite element approximation space with time. An analysis of how this method models the steady solutions of a general class of parabolic linear source equations is presented. It is shown that the steady solutions of the Moving F...

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 ...

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...

modelling of crack propagation by finite element method under mixed mode conditions is of prime importance in fracture mechanics. this paper describes an application of finite element method to the analysis of mixed mode crack growth in linear elastic fracture mechanics. crack growth process is simulated by an incremental crack-extension analysis based on the maximum principal stress criterion,...