This paper deals with the finite element solution of the convection diffusion equation in one and two dimensions. Two main techniques are adopted and compared. The first one includes Petrov-Galerkin based on Lagrangian tensor product elements in conjunction with streamlined upwinding. The second approach represents Bubnov/Petrov-Galerkin schemes based on a new group of exponential elements. It ...

A finite-element deformable surface-spine model is developed in this paper to register two surfaces by recovering the nonlinear deformation with respect to each other. The deformable surface-spine model is a dynamic model governed by Lagrangian motion equations. A 9 degree-of-freedom (dof) finite-element surface element and a $-dof spine element are developed to iteratively solve Lagrangian equ...

The standard in rod finite element formulations is the Bubnov–Galerkin projection method, where test functions arise from a consistent variation of ansatz functions. This approach becomes increasingly complex when highly nonlinear are chosen to approximate rod's centerline and cross-section orientations. Using Petrov–Galerkin we propose whole family nodal generalized virtual displacements veloc...

This paper introduces a Semi-Lagrangian solver for the Vlasov-Poisson equations on a uniform hexagonal mesh. The latter is composed of equilateral triangles, thus it doesn’t contain any singularities, unlike polar meshes. We focus on the guiding-center model, for which we need to develop a Poisson solver for the hexagonal mesh in addition to the Vlasov solver. For the interpolation step of the ...

In this work, the finite element simulation of dissimilar friction stir welding process is investigated. The welded materials are AA 6061-T6 and AA 7075-T6 aluminum alloys. For this purpose, a 3D coupled thermo-mechanical finite element model is developed according to the Coupled Eulerian-Lagrangian (CEL) method. The CEL method has the advantages of both Lagrangian and Eulerian approaches, whic...

For the purpose of surgical simulation, we propose an algorithm based upon the Element Free Galerkin method, Total Lagrangian explicit dynamics and nonlinear material formulation. The proposed algorithm does not require a finite element mesh, so is well suited to simulations with irregular geometry. As an example, a simplified 3D simulation of craniotomy induced brain shift including brain, ven...

a non-linear finite element model could be a useful tool in the development of a method of predicting soil pressure-sinkage behaviour, and can be used to investigate and analyze soil compaction. this study was undertaken to emphasize that the finite element method (fem) is a proper technique to model soil pressure-sinkage behaviour. for this purpose, the finite element method was used to model ...

The possibility to use a Lagrangian frame to solve problems with large time-steps was successfully explored previously by the authors for the solution of homogeneous incompressible fluids and also for solving multi-fluid problems [28-30]. The strategy used by the authors was named Particle Finite Element Method second generation (PFEM-2). The objective of this paper is to demonstrate in which c...