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...

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...

We introduce a new and eecient Chebyshev-Legendre Galerkin method for elliptic problems. The new method is based on a Legendre-Galerkin formulation, but only the Chebyshev-Gauss-Lobatto points are used in the computation. Hence, it enjoys advantages of both the Legendre-Galerkin and Chebyshev-Galerkin methods.

In this article, we prove convergence of the weakly penalized adaptive discontinuous Galerkin methods. Unlike other works, we derive the contraction property for various discontinuous Galerkin methods only assuming the stabilizing parameters are large enough to stabilize the method. A central idea in the analysis is to construct an auxiliary solution from the discontinuous Galerkin solution by ...

Proliferation of degrees-of-freedom has plagued discontinuous Galerkin methodology from its inception over 30 years ago. This paper develops a new computational formulation that combines the advantages of discontinuous Galerkin methods with the data structure of their continuous Galerkin counterparts. The new method uses local, element-wise problems to project a continuous finite element space ...

The concept of a stress tensor [for instance, the Cauchy stress σ , Cauchy (1789-1857); the first Piola-Kirchhoff stress P, Piola (1794-1850), and Kirchhoff (1824-1889); and the second Piola-Kirchhoff stress, S] plays a central role in Newtonian continuum mechanics, through a physical approach based on the conservation laws for linear and angular momenta. The pioneering work of Noether (1882-19...