Discontinuous Galerkin spatial discretisation of the neutron transport equation with pyramid finite elements and a discrete ordinate (SN) angular approximation

On discontinuous Galerkin and discrete ordinates approximations for neutron transport equation and the critical eigenvalue

Discrete-Ordinate Discontinuous Galerkin Methods for Solving the Radiative Transfer Equation

Abstract. The radiative transfer equation (RTE) occurs in a wide variety of applications. In this paper, we study discrete-ordinate discontinuous Galerkin methods for solving the RTE. The numerical methods are formed in two steps. In the first step, the discrete ordinate technique is applied to discretize the integral operator for the angular variable, resulting in a semi-discrete hyperbolic sy...

Convergence of a Discontinuous Galerkin Scheme for the Neutron Transport

We study the spatial discretization for the numerical solution of a model problem for the neutron transport equation in an innnite cylindrical media. Based on using an interpolation technique in the discontinuous Galerkin nite element procedure, and regulariz-ing properties of the solution operator, we derive an optimal error estimate in L 2 ?norm for the scalar ux. This result, combined with a...

Discontinuous Galerkin Discretization and hp-Refinement for the Resolution of the Neutron Transport Equation

Discontinuous Galerkin Finite Element Approximation of the Cahn-Hilliard Equation with Convection

The paper is concerned with the construction and convergence analysis of a discontinuous Galerkin finite element method for the Cahn–Hilliard equation with convection. Using discontinuous piecewise polynomials of degree p ≥ 1 and backward Euler discretization in time, we show that the order-parameter c is approximated in the broken L∞(H1) norm with optimal order, O(hp+ τ); the associated chemic...