A general review of the extended finite element method and its application to the simulation of first-order phase transitions is provided. Detailed numerical investigations are then performed by focusing on the one-dimensional case and studying: (i) spatial and temporal discretisations, (ii) different numerical techniques for the interface-condition enforcement, and (iii) different treatments f...

An algorithm for non-intrusively coupling a commercial finite element software with a research code implementing a hierarchical enrichment of finite element spaces is presented. Examples of hierarchical methods supported by the algorithm are the Generalized or eXtended FEM (GFEM), the scale-bridging GFEM with numerically defined enrichment functions (GFEMgl), and the p-version of the FEM. The p...

In this paper, the extended finite element method (X-FEM) is considered for the analysis of fretting fatigue problems. A two-dimensional implementation of the XFEM is carried out within the finite element software ABAQUS by means of user subroutines, and crack propagation in fretting fatigue problems is investigated. On utilizing the non-linear contact capabilities of this code, the numerical t...

A mapping method is developed to integrate weak singularities which result from enrichment functions in the generalized/extended FEM. The integration scheme is applicable to 2D and 3D problems including arbitrarily shaped triangles and tetrahedra. Implementation of the proposed scheme in existing codes is straightforward. Numerical examples for 2D and 3D problems demonstrate the accuracy and co...

The purpose of this paper is to present a new fictitious domain approach inspired by the extended finite element method introduced by Moës, Dolbow and Belytschko in [18]. An optimal method is obtained thanks to an additional stabilization technique. Some a priori estimates are established and numerical experiments illustrate different aspects of the method. The presentation is made on a simple ...

The recovery type error estimators introduced by Zienkiewicz and Zhu use a recovered stress field evaluated from the Finite Element (FE) solution. Their accuracy depends on the quality of the recovered field. In this sense, accurate results are obtained using recovery procedures based on the Superconvergent Patch Recovery technique (SPR). These error estimators can be easily implemented and pro...

We propose an efficient computational method to simulate two-phase flow in fractured porous media. Instead of refining the grid to capture the flow along the faults or fractures, we represent them as immersed interfaces with reduced model for the flow and suitable coupling conditions. We allow for non matching grids between the porous matrix and the fracture to increase the flexibility of the m...