We propose a new family of finite element methods for the Naghdi shell model, one method associated with each nonnegative integer k. The methods are based on a nonstandard mixed formulation, and the kth method employs triangular Lagrange finite elements of degree k+2 augmented by bubble functions of degree k+ 3 for both the displacement and rotation variables, and discontinuous piecewise polyno...

We propose a new formulation along with a family of finite element schemes for the approximation of the interaction between fluid motion and linear mechanical response of a porous medium, known as Biot’s consolidation problem. The steady-state version of the system is recast in terms of displacement, pressure, and volumetric stress, and both continuous and discrete formulations are analyzed as ...

To solve crack problems, some coupled methods have been developed in recent years. Most of these methods have some shortcomings such as the need for a transition region. The finite element and enriched element free Galerkin methods are widely used for this class of problems. In order to take the advantages of these methods while avoiding the disadvantages, it is essential to follow solution app...

a new approach for analyzing cracked problems in 2d orthotropic materials using the well-known element free galerkin method and orthotropic enrichment functions is proposed. the element free galerkin method is a meshfree method which enables discontinuous problems to be modeled efficiently. in this study, element free galerkin is extrinsically enriched by the recently developed crack-tip orthot...