This paper presents and studies a residual a posteriori error estimator for Laplace’s equation in two space dimensions approximated by the eXtended Finite Element Method (XFEM). The XFEM allows to perform finite element computations on multi-cracked domains by using meshes of the non-cracked domain. The main idea consists of adding supplementary basis functions of Heaviside type and singular fu...

We consider a standard sharp interface model for the fluid dynamics in a twophase incompressible flow, combined with a convection-diffusion model for solute transport. Some important numerical challenges related to these models are discussed. We present a finite element discretization method for the solute transport model. The method is based on an Eulerian approach, i.e. computational grids ar...

TheG-function approach to premixed combustion problems is based on the flamelet concept. Thereby, the flame front is modeled as an embedded interface within the bulk. A level set function is used to describe the position of the flame front. To account for discontinuities in the velocity and the pressure fields across the interface, an eXtended Finite Element Method (XFEM) is applied. That is, t...

The development of the computational techniques used in the analyzes of the dynamic fracture and their implementation in numerical codes takes a growing importance in last years. This interest derives from the necessity to predict the localisation of the initiations of cracks, when and in which direction this crack will propagate throw the material under dynamic loads. Several numerical approac...

In this paper, the extended finite element method (XFEM) is first applied to account for weak discontinuity of axisymmetric electrostatic field. Firstly, interface between two materials in an described by level set method. The enrichment function used modify shape elements. Secondly, illustrate feature function, distribution diagrams functions sub-elements are drawn. 3D field can be simplified ...

The present work investigates the effect of the elliptical three-dimensional (3D) cracks on a pipe with thickness transition, considering internal pressure. Level sets were defined using the extended finite element method (XFEM), the stress intensity factors (SIFs) of 3D cracks were investigated and compared between straight pipes and pipes with thickness transition. The results show that the X...

Fluid-solid coupling is ubiquitous in the process of fluid flow underground and has a significant influence on the development of oil and gas reservoirs. To investigate these phenomena, the coupled mathematical model of solid deformation and fluid flow in fractured porous media is established. In this study, the discrete fracture model (DFM) is applied to capture fluid flow in the fractured por...

We consider a standard model for incompressible two-phase flows in which a localized force at the interface describes the effect of surface tension. If a level set (or VOF) method is applied then the interface, which is implicitly given by the zero level of the level set function, is in general not aligned with the triangulation that is used in the discretization of the flow problem. This nonal...

This paper develops the extended finite element method (XFEM) to evolve patterns of multiple cracks, in a brittle thin film bonded to an elastic substrate, with a relatively coarse mesh, and without remeshing during evolution. A shear lag model describes the deformation in three dimensions with approximate field equations in two-dimensions. The film is susceptible to subcritical cracking, obeyi...