In this paper, we propose an extended mixed finite element method for elasticity interface problems based on Mini space. The stabilization term defined edges of elements and the ghost penalty are added, which ensures that discrete inf-sup condition holds independent how intersects triangulation. Finally, numerical experiments carried out to verify theoretical analysis.

Deformable fractured porous media appear in many geoscience applications. While the extended finite element (XFEM) has been successfully developed within computational mechanics community for accurate modeling of deformation, its application natural geoscientific applications is not straightforward. This mainly due to fact that subsurface formations are heterogeneous and span large length scale...

In this paper, we propose an extended mixed finite element method for elliptic interface problems. By adding some stabilization terms, present a approximation form based on Brezzi-Douglas-Marini space and the piecewise constant function space, show that discrete inf-sup is independent of how intersects triangulation. Furthermore, derive optimal convergence holds location relative to mesh. Final...

We consider a space-time finite element discretization of a time-dependent nonlinear hyperbolic conservation law in one space dimension (Burgers' equation). The finite element method is higher-order accurate and is a Petrov-Galerkin method based on the so-called streamline diffusion modification of the test functions giving added stability. We first prove that if a sequence of finite element so...

1. Abstract In this paper, we implement the extended finite element method (X-FEM) combined with the level set method to solve structural shape and topology optimization problems. Numerical comparisons with the conventional finite element method in a fixed grid show that the X-FEM leads to more accurate results without increasing the mesh density and the degrees of freedom. Furthermore, the mes...