This note revisits the derivation of the ALE form of the incompressible Navier-Stokes equations in order to retain insight into the nature of geometric conservation. It is shown that the flow equations can be written such that time derivatives of integrals over moving domains are avoided prior to discretisation. The geometric conservation law is introduced into the equations and the resulting f...

(1) A one-dimensional minimization problem and the Ritz method. (2) Weak formulation and the Galerkin method. Abstract error estimates. (3) The lemma of variations. Euler-Lagrange equations. Weak formulation, again. (4) The Ritz-Galerkin finite element method: philosophy. (5) The piecewise linear finite element space and basis functions. The linear system. (6) The piecewise linear finite elemen...

We construct finite element subspaces of the space of symmetric tensors with square-integrable divergence on a three-dimensional domain. These spaces can be used to approximate the stress field in the classical Hellinger–Reissner mixed formulation of the elasticty equations, when standard discontinuous finite element spaces are used to approximate the displacement field. These finite element sp...

Original scientific paper Finite difference procedures for flux determination are not well suited for application to field results obtained from finite element calculations. A novel method for flux calculation has been derived. This method is based on the weak formulation and is suitable for use with finite elements. A matrix formulation for local and global application to finite element formul...

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 paper, the finite element analysis of two-dimensional linear viscoelastic problems is performed using quadrilateral complex Fourier elements and, the results are compared with those obtained by quadrilateral classic Lagrange elements. Complex Fourier shape functions contain a shape parameter which is a constant unknown parameter adopted to enhance approximation’s accuracy. Since the iso...

Abstract This work describes the implementation of a novel dynamic Arbitrary Lagrangian Eulerian (ALE) formulation for simulation pavement structures loaded by rolling tires in finite element framework. The proposed enables effects like acceleration, deceleration and variation wheel load on pavement. ALE scheme is described hyperelastic St. Venant-Kirchhoff material capable deformations. With a...

analysis of the stresses, displacements, and horizontal strains of the ground subsidence due to underground excavation in rocks can be accomplished by means of a hybridized higher order indirect boundary element/finite difference (be/fd) formulation. a semi-infinite displacement discontinuity field is discretized (numerically) using the cubic displacement discontinuity elements (i.e. each highe...