A meshless approach to the analysis of arbitrary Kirchhoff shells by the Element-Free Galerkin (EFG) method is presented. The shell theory used is geometrically exact and can be applied to deep shells. The method is based on moving least squares approximant. The method is meshless, which means that the discretization is independent of the geometric subdivision into “finite elements”. The satisf...

For nearly incompressible elasticity, volumetric locking is a well-known phenomenon with low-order (cubic or lower) fi nite element method methods, of which continuous extended fi nite element methods (XFEMs) are no exception. We will present an XFEM that is simultaneously lock-free and optimally convergent. Based on our earlier work of an optimally convergent discontinuous-Galerkin-based XFEM,...

An oscillation free local discontinuous Galerkin (OFLDG) method is proposed for solving nonlinear degenerate parabolic equations. The damping terms are added to the original LDG scheme control spurious oscillations when solutions have a large gradient. L2-stability and optimal priori error estimates semi-discrete in one- multi-dimensions established. numerical experiments demonstrate that maint...

In this paper, we study a mesh-free method using the Galerkin method with radial basis functions (RBFs) for the exterior Neumann problem of the Laplacian with boundary condition on an oblate spheroid. This problem is reformulated as a pseudo-differential equation on the spheroid by using the Dirichlet-to-Neumann map. We show convergence of the Galerkin scheme. Our approach is particularly suita...

in this paper, the ritz-galerkin method in bernstein polynomial basis is applied for solving the nonlinear problem of the magnetohydrodynamic (mhd) flow of third grade fluid between the two plates. the properties of the bernstein  polynomials together with the ritz-galerkin method are used to reduce the solution of the mhd couette flow of non-newtonian fluid in a porous medium to the solution o...