An analytical method for approximating high-order Galerkin solutions

High order quadrature based iterative method for approximating the solution of nonlinear equations

In this paper, weight function and composition technique is utilized to speeds up the convergence order and increase the efficiency of an existing quadrature based iterative method. This results in the proposition of its improved form from a two-point quadrature based method of convergence order ρ = 3 with efficiency index EI = 1:3161 to a three-point method of convergence order ρ = 8 with EI =...

High-Order Discontinuous Galerkin Method on Hexahedral Elements for Aeroacoustics High-Order Discontinuous Galerkin Method on Hexahedral Elements for Aeroacoustics

High-order Analytical Solutions of Hill’s Equations

The purpose of this paper is the semi-analytical computation of the bounded orbits of Hill’s equations, describing the relative motion of two particles in their Keplerian motion around a central body. We have considered the case in which one of the particles moves along a circular reference orbit. The solutions obtained are the generalisation of the usual periodic orbits obtained for the linear...

Positivity preserving high-order local discontinuous Galerkin method for parabolic equations with blow-up solutions

Article history: Received 13 October 2014 Received in revised form 17 January 2015 Accepted 18 February 2015 Available online 2 March 2015

Arbitrary High-order Discontinuous Galerkin Method for Electromagnetic Field Problems

In this paper, we present a time integration scheme applied to the Discontinuous Galerkin finite element method (DG-FEM, [1]) for the computation of electromagnetic fields in the interior of three-dimensional structures. This approach is also known as Arbitrary High-Order Derivative Discontinuous Galerkin (ADER-DG, [2, 3]). By this method, we reach arbitrary high accuracy not only in space but ...