In this paper, elasto-plastic analysis of an edge crack has been performed using element free Galerkin method. A model problem has been solved in plane stress condition under mode-I loading. A system of nonlinear equations has been obtained by using incremental theory of plasticity, and the equations are solved by assuming piecewise linear approximation. A code has been written in Matlab for el...

The formulation and the implementation of boundary conditions within the context of the quadrature-free form of the discontinuous Galerkin method are presented for several types of boundary conditions for the Euler equations. An important feature of the discontinuous Galerkin method is that the interior point algorithm is well behaved in the neighborhood of the boundary and requires no modi cat...

We present an adaptive spacetime discontinuous Galerkin (SDG) method for linearized elastodynamics. The SDG method uses a simple Bubnov-Galerkin projection that delivers stable and oscillation–free solutions, with O (N) complexity and exact momentum balance on every spacetime element. An extended version of the Tent Pitcher algorithm generates unstructured spacetime grids that support simultane...

A new family of Petrov-Galerkin nite element methods on triangular grids is constructed for singularly perturbed elliptic problems in two dimensions. It uses divergence-free trial functions that form a natural generalization of one-dimensional exponential trial functions. This family includes an improved version of the divergence-free nite element method used in the PLTMG code. Numerical result...

We present a higher order accurate discontinuous Galerkin finite element method for the simulation of linear free-surface gravity waves. The method uses the classical Runge-Kutta method for the time discretization of the free-surface equations and the discontinuous Galerkin method for the space discretization. In order to circumvent numerical instabilities arising from an asymmetric mesh a stab...