A novel spectral element technique is examined in which the test functions are different from the approximating elements. Examples are given for a simple 1D Helmholtz equation, Burger's Equation with a small viscosity, and for Darcy's Equation with a discontinous hydraulic conductivity. 1. Polynomial Approximation. Spectral element approximations have been shown to be an eeective tool for the a...

A Meshless Local Petrov-Galerkin (MLPG) method has been developed for solving 3D elastodynamic problems. It is derived from the local weak form of the equilibrium equations by using the general MLPG concept. By incorporating the moving least squares (MLS) approximations for trial and test functions, the local weak form is discretized, and is integrated over the local sub-domain for the transien...

In this study we develop a formalism to describe the organization of DNA inside bacteriophage capsids during genome packaging. We have previously shown that DNA inside bacteriophage phi29 (phi29) is organized into folded toroids [A. S. Petrov and S. C. Harvey, Structure 15, 21 (2007)], whereas epsilon15 (epsilon15) reveals the coaxial organization of the genetic material [A. S. Petrov, K. Lim-H...

We introduce a new family of integrable stochastic processes, called dynamical stochastic higher spin vertex models, arising from fused representations of Felder’s elliptic quantum group Eτ,η(sl2). These models simultaneously generalize the stochastic higher spin vertex models, studied by Corwin-Petrov and Borodin-Petrov, and are dynamical in the sense of Borodin’s recent stochastic interaction...

This paper considers the numerical solution of time-dependent convection-diffusion-reaction equations. We shall employ combinations of streamlineupwind Petrov–Galerkin (SUPG) and local projection stabilization (LPS) meth-ods in space with the higher order variational time discretization schemes. In particular, we consider time discretizations by discontinuous Galerkin (dG) meth-ods and continuo...

This paper is an attempt in seeking a connection between the discontinuous Petrov– Galerkin method of Demkowicz and Gopalakrishnan [13,15] and the popular discontinuous Galerkin method. Starting from a discontinuous Petrov–Galerkin (DPG) method with zero enriched order we re-derive a large class of discontinuous Galerkin (DG) methods for first order hyperbolic and elliptic equations. The first ...

(2001) A Meshless Local Petrov-Galerkin (MLPG) method for free and forced vibration analyses for solids. Abstract The Meshless Local Petrov-Galerkin (MLPG) method is an effective truly meshless method for solving partial differential equations using Moving Least Squares (MLS) interpolants and local weak forms. In this paper, a MLPG formulation is proposed for free and forced vibration analyses....

We investigate the numerical solution of an integro-differential equation with a memory term. For the time discretization we apply the continuous Petrov–Galerkin method considered by Lin et al. [SIAM J. Numer. Anal., 38, 2000]. We combined the Petrov–Galerkin scheme with respect to time with continuous finite elements for the space discretization and obtained a fully discrete scheme. We show op...