A positivity-preserving semi-implicit discontinuous Galerkin scheme for solving extended magnetohydrodynamics equations

A positivity-preserving semi-implicit discontinuous Galerkin scheme for solving extended magnetohydrodynamics equations

Article history: Received 26 February 2014 Received in revised form 20 August 2014 Accepted 26 August 2014 Available online 3 September 2014

A semi-implicit, semi-Lagrangian, p-adaptive discontinuous Galerkin method for the shallow water equations

Article history: Received 21 February 2012 Received in revised form 30 May 2012 Accepted 4 June 2012 Available online 16 June 2012

Implicit Positivity-Preserving High-Order Discontinuous Galerkin Methods for Conservation Laws

A Positivity-Preserving Well-Balanced Central Discontinuous Galerkin Method for the Nonlinear Shallow Water Equations

In this paper, we consider the development of central discontinuous Galerkin methods for solving the nonlinear shallow water equations over variable bottom topography in one and two dimensions. A reliable numerical scheme for these equations should preserve still-water stationary solutions and maintain the non-negativity of the water depth. We propose a high-order technique which exactly balanc...

Positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations with source terms

In [16, 17], we constructed uniformly high order accurate discontinuous Galerkin (DG) schemes which preserve positivity of density and pressure for the Euler equations of compressible gas dynamics with the ideal gas equation of state. The technique also applies to high order accurate finite volume schemes. For the Euler equations with various source terms (e.g., gravity and chemical reactions),...