We consider a standard model for mass transport across an evolving interface. The solution has to satisfy a jump condition across an evolving interface. In the recent paper [C. Lehrenfeld, A. Reusken, SIAM J. Num. Anal., 51 (2013)] a new finite element discretization method for this mass transport problem is presented and analyzed. This method is based on a space-time approach in which a discon...

We consider a standard model for mass transport across an evolving interface. The solution has to satisfy a jump condition across an evolving interface. We present and analyze a finite element discretization method for this mass transport problem. This method is based on a space-time approach in which a discontinuous Galerkin (DG) technique is combined with an extended finite element method (XF...

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A numerical technique for planar three-dimensional fatigue crack growth simulations is proposed. The new technique couples the extended finite element method (X-FEM) to the fast marching method (FMM). In the X-FEM, a discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are added to the finite element approximation to account for the crack using the notion of p...

This study presents a fast and exact computational method for crack propagation which is based on the extended finite element method (X-FEM). It is well known that the X-FEM has been developed to be an important numerical method for crack propagation. However, there are still some limitations on the computational cost due to the requirements of very refined meshes and very small iteration step ...

We consider a standard model for mass transport across an evolving interface. The solution has to satisfy a jump condition across an evolving interface. We present and analyze a finite element discretization method for this mass transport problem. This method is based on a space-time approach in which a discontinuous Galerkin (DG) technique is combined with an extended finite element method (XF...

In the present paper we consider a 1D Poisson model characterized by the presence of an interface, where a transmission condition arises due to jumps of the coefficients. We aim at studying finite element methods with meshes not fitting such an interface. It is well known that when the mesh does not fit the material discontinuities the resulting scheme provides in general lower order accurate s...

Rapid development of engineering activities expands through a variety of rock engineering processes such as drilling, blasting, mining and mineral processing. These activities require rock dynamic fracture mechanics method to characterize the rock behavior. Dynamic fracture toughness is an important parameter for the analysis of engineering structures under dynamic loading. Several experimental...