We are interested in developing a numerical framework well suited for advectiondiffusion problems when the advection part is dominant. In that case, given Dirichlet type boundary condition, it is well known that a boundary layer develops. In order to resolve correctly this layer, standard methods consist in increasing the mesh resolution and possibly increasing the formal accuracy of the numeri...

Reliable numerical simulation of failure is important for the design and planning of new solids and structures, as well as for the safety assessment of existing ones. In the past two decades, gradient and non-local models for regularizing loss of ellipticity due to material failure using non-standard finite element method and more recently the meshfree method have been the topic of considerable...

The elastic-plastic behavior of the material is considered to analyze the effect of an external circumferential crack on a pipe with thickness transition and double slopes. Using the extended finite element method (XFEM), the J-integral of 3D cracks were investigated and compared between straight pipes and pipes with thickness transition and different slopes. Considering internal press...