Related papers: On the TVD property of second order methods for 2D…
This paper investigates some properties of entropy solutions of hyperbolic conservation laws on a Riemannian manifold. First, we generalize the Total Variation Diminishing (TVD) property to manifolds, by deriving conditions on the flux of…
Little is known about global existence of large-variation solutions to Cauchy problems for systems of conservation laws in one space dimension. Besides results for $L^\infty$ data via compensated compactness, the existence of global BV…
2D Total Variation Denoising (TVD) is a widely used technique for image denoising. It is also an important nonparametric regression method for estimating functions with heterogenous smoothness. Recent results have shown the TVD estimator to…
This paper proposes a first-order total variation diminishing (TVD) treatment for coarsening and refining of local timestep size in response to dynamic local variations in wave speeds for nonlinear conservation laws. The algorithm is…
The total variation (TV)-seminorm is considered for piecewise polynomial, globally discontinuous (DG) and continuous (CG) finite element functions on simplicial meshes. A novel, discrete variant (DTV) based on a nodal quadrature formula is…
A general procedure to construct a class of simple and efficient high resolution Total Variation Diminishing (TVD) schemes for non-linear hyperbolic conservation laws by introducing anti-diffusive terms with the flux limiters is presented.…
The Van Leer approach for the approximation of nonlinear scalar conservation laws is studied in one space dimension. The problem can be reduced to a nonlinear interpolation and we propose a convexity property for the interpolated values. We…
This paper describes a multidimensional hydrodynamic code which can be used for studies of relativistic astrophysical flows. The code solves the special relativistic hydrodynamic equations as a hyperbolic system of conservation laws based…
A second-order total variation diminishing (TVD) method with variable flux limiters is proposed to overcome the non-realizability issue, which has been one of major obstacles in applying the conventional second-order TVD schemes to the…
For finite element approximations of transport phenomena, it is often necessary to apply a form of limiting to ensure that the discrete solution remains well-behaved and satisfies physical constraints. However, these limiting procedures are…
We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…
We present a novel quasi-conservative arbitrary high order accurate ADER discontinuous Galerkin (DG) method allowing to efficiently use a non-conservative form of the considered partial differential system, so that the governing equations…
The flux vector splitting (FVS) method has firstly been incorporated into the discontinuous Galerkin (DG) framework for reconstructing the numerical fluxes required for the spatial semi-discrete formulation, setting it apart from the…
In this paper, we develop a family of high order cut discontinuous Galerkin (DG) methods for hyperbolic conservation laws in one space dimension. The ghost penalty stabilization is used to stabilize the scheme for small cut elements. The…
The main contribution of this work is to construct higher than second order accurate total variation diminishing (TVD) schemes which can preserve high accuracy at non-sonic extrema with out induced local oscillations. It is done in the…
In this work, we consider the development of implicit explicit total variation diminishing (TVD) methods (also termed SSP: strong stability preserving) for the compressible isentropic Euler system in the low Mach number regime. The scheme…
The purpose of this work is to propose a novel a posteriori finite volume subcell limiter technique for the Discontinuous Galerkin finite element method for nonlinear systems of hyperbolic conservation laws in multiple space dimensions that…
We present a novel class of locally conservative, entropy stable and well-balanced discontinuous Galerkin (DG) methods for the nonlinear shallow water equation with a non-flat bottom topography. The major novelty of our work is the use of…
We present a second-order accurate numerical method for a class of nonlocal nonlinear conservation laws called the "nonlocal pair-interaction model" which was recently introduced by Du, Huang, and LeFloch. Our numerical method uses…
A moving mesh discontinuous Galerkin method is presented for the numerical solution of hyperbolic conservation laws. The method is a combination of the discontinuous Galerkin method and the mesh movement strategy which is based on the…