We develop a new formulation of the Control Volume Finite Element Method (CVFEM) with a multidimensional Scharfetter-Gummel (SG) upwinding for the drift-diffusion equations. The formulation uses standard nodal elements for the concentrations and expands the flux in terms of the lowest-order Nedelec H(curl,Ω)-compatible finite element basis. The SG formula is applied to the edges of the elements...

A spatial geometrically exact finite element based on the fixed-pole approach of an arbitrary order is presented. In contrast to the original formulation by Bottasso and Borri, this formulation uses standard kinematic unknowns and is therefore combinable with standard finite elements. Preliminary results show that when updating displacements and rotations at integration points, this formulation...

The paper will review the art, craft and science of modelling cavitation bubbles near boundaries through the use of the boundary integral method. The presentation will come in four parts, namely, a discussion of recent experimental studies that have motivated our current research, understanding the physics associated with the phenomena, a detailed presentation on the boundary integral method an...

A formulation and an implementation of two-dimensional Boundary Element Method (BEM) analysis for steady state, uncoupled thermoelastic problems is presented. This approach differs from other treatments of thermal loads in BEM analysis in which the domain integrals due to the thermal gradients are to be incorporated in the analysis via particular-integrals. Thus unlike Finite Elements or Field ...

Wave propagation in unbounded layered media with a new formulation of Axisymmetric Scaled Boundary Finite Element Method (AXI-SBFEM) is derived. Dividing the general three-dimensional unbounded domain into a number of independent two-dimensional ones, the problem could be solved by a significant reduction in required storage and computational time. The equations of the corresponding Axisymmetri...

In this work, we analyze a recently proposed stabilized finite element formulation for the approximation of the resistive magnetohydrodynamics equations. The novelty of this formulation with respect to existing ones is the fact that it always converges to the physical solution, even when it is singular. We have performed a detailed stability and convergence analysis of the formulation in a simp...

A new mixed, stabilized, discontinuous Galerkin formulation for Darcy flow is presented. The formulation combines several attributes not simultaneously satisfied by other methods: It is convergent for any combination of velocity and pressure interpolation higher than first-order, it exactly satisfies a mass balance on each element, and it passes twoand three-dimensional constant-flow ‘‘patch te...

In this paper, a self-consistent boundary element method is introduced to predict overall properties of a cracked bimaterial plate. The boundary element (BE) formulation is developed based on Green’s function for displacement discontinuity of a bimaterial solid and potential variational principles. The self-consistent method is then introduced into the BE formulation to provide an effective mea...