A Riemann-Solver Free Spacetime Discontinuous Galerkin Method for General Conservation Laws

Riemann solutions for spacetime discontinuous Galerkin methods

Spacetime discontinuous Galerkin finite element methods [1–3] rely on ‘target fluxes’ on elementboundaries that are computed via local one-dimensional Riemann solutions in the direction normal toelement face. In this work, we demonstrate a generalized solution procedure for linearized hyperbolicsystems based on diagonalisation of the governing system of partial differential equa...

Moving Mesh Discontinuous Galerkin Method for Hyperbolic Conservation Laws

In this paper, a moving mesh discontinuous Galerkin (DG) method is developed to solve the nonlinear conservation laws. In the mesh adaptation part, two issues have received much attention. One is about the construction of the monitor function which is used to guide the mesh redistribution. In this study, a heuristic posteriori error estimator is used in constructing the monitor function. The se...

The Runge–Kutta Discontinuous Galerkin Method for Conservation Laws V

This is the fifth paper in a series in which we construct and study the so-called Runge–Kutta discontinuous Galerkin method for numerically solving hyperbolic conservation laws. In this paper, we extend the method to multidimensional nonlinear systems of conservation laws. The algorithms are described and discussed, including algorithm formulation and practical implementation issues such as the...

The Discontinuous Galerkin Method for Fractal Conservation Laws

We propose, analyze, and demonstrate a discontinuous Galerkin method for fractional conservation laws. Various stability estimates are established along with error estimates for regular solutions of linear equations. Moreover, in the nonlinear case and when piecewise constant elements are utilized, we prove a rate of convergence toward the unique entropy solution. We present numerical results f...

The Runge-Kutta discontinuous Galerkin method for conservation laws V: . . .