SUMMARYA minimal remeshing ÿnite element method for crack growth is presented. Discontinuous enrichment functions are added to the ÿnite element approximation to account for the presence of the crack. This method allows the crack to be arbitrarily aligned within the mesh. For severely curved cracks, remeshing may be needed but only away from the crack tip where remeshing is much easier. Results are presented for a wide range of two-dimensional crack problems showing excellent accuracy.

No abstract

In this article we investigate a parabolic-parabolic-elliptic two-species chemotaxis system with weak competition and show global asymptotic stability of the coexistence steady state under a smallness condition on the chemotactic strengths, which seems more natural than the condition previously known. For the proof we rely on the method of eventual comparison, which thereby is shown to be a useful tool even in the presence of chemotactic terms.

The application of a coupled ®nite element± element-free Galerkin (EFG) method to problems in threedimensional fracture is presented. The EFG method is based on moving least square (MLS) approximations and uses only a set of nodal points and a CAD-like description of the body to formulate the discrete model. The EFG method is coupled with the ®nite element method which allows for the use of the EFG method in the crack region and the ®nite element method to model the remainder of the problem. Domain integral methods are used to evaluate stress intensity factors along the 3D crack front. Both planar and volume representations of the domain integrals are considered. The former require derivatives of stress and strain which are readily obtainable in the EFG method due to the C 1 continuity of the MLS approximations used here. Applications of the method to the determination of stress intensity factors along planar cracks in 3D are presented.

Abstract. In bounded smooth domains Ω ⊂ R N , N ∈ {2, 3} considering the chemotaxis-fluid systemwith singular sensitivity, we prove global existence of classical solutions for given φ ∈ C 2 (Ω), for κ = 0 (Stokes-fluid) if N = 3 and κ ∈ {0, 1} (Stokes-or NavierStokes fluid) if N = 2 and under the condition thatMSC (