A front tracking method for conservation laws in one dimension

A Conservative Front Tracking Method for Hyperbolic Conservation Laws

Further Development of a Conservative Front-Tracking Method for Systems of Conservation Laws in One Space Dimension

In this paper, we further analyze, improve and develop the conservative fronttracking method developed in Mao(1995, SIAM. J. Numer. Anal., 32, 1677– 1703). The method in Mao(1995, SIAM. J. Numer. Anal., 32, 1677–1703) is only first-order accurate near the tracked discontinuities when applied to systems of conservation laws. This is because in the system case near tracked discontinuities there a...

A Front Tracking Method for Compressible Flames in One Dimension

Abstract. A numerical method is presented for the treatment of one-dimensional compressible flames. The method consists of a conservative front tracking algorithm for use near the flame and a high-order finite difference scheme for capturing the hvdrodynamics throughout the rest of the domain. The results presented show that the method effectively models the interaction of gas dynamics with bot...

Superconvergence of Discontinuous Galerkin Method for Scalar Nonlinear Conservation Laws in One Space Dimension

Abstract. In this paper, the analysis of the superconvergence property of the discontinuous Galerkin (DG) method applied to one-dimensional time-dependent nonlinear scalar conservation laws is carried out. We prove that the error between the DG solution and a particular projection of the exact solution achieves (k+ 3 2 )-th order superconvergence when upwind fluxes are used. The results hold tr...

Arbitrary Lagrangian-Eulerian discontinuous Galerkin method for conservation laws: Analysis and application in one dimension

In this paper, we develop and analyze an arbitrary Lagrangian-Eulerian discontinuous Galerkin (ALE-DG) method with a time-dependent approximation space for one dimensional conservation laws, which satisfies the geometric conservation law. For the semi-discrete ALE-DG method, when applied to nonlinear scalar conservation laws, a cell entropy inequality, L2 stability and error estimates are prove...