Browsing by Author "Shu, Chi-Wang"
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Item The development of discontinuous Galerkin methods(1999-12) Cockburn, Bernardo; Karniadakis, George E.; Shu, Chi-WangItem The local discontinuous Galerkin method for time-dependent convection-diffusion systems(1997-03) Cockburn, B.; Shu, Chi-WangItem Mixed-RKDG finite element methods for the 2-D hydrodynamic model for semiconductor device simulation(1992-12) Chen, Zhangxin; Cockburn, Bernardo; Jerome, Joseph W.; Shu, Chi-WangItem The Runge-Kutta Discontinuous Galerkin Method for Conservation Laws V: Multidimensional Systems(1997-06) Cockburn, B.; Shu, Chi-WangItem Runge-Kutta discontinuous Galerkin methods for convection-dominated problems(2000-12) Cockburn, Bernardo; Shu, Chi-WangIn this paper, we review the development of the Runge-Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge-Kutta time discretizations, that allows the method to be non-linearly stable regardless of its accuracy, with a finite element space discretization by discontinuous approximations, that incorporates the ideas of numerical fluxes and slope limiters coined during the remarkable development of the high-resolution finite difference and finite volume schemes. The resulting RKDG methods are stable, high-order accurate, and highly parallelizable schemes that can easily handle complicated geometries and boundary conditions. We review the theoretical and algorithmic aspects of these methods and show several applications including nonlinear conservation laws, the compressible and incompressible Navier-Stokes equations, and Hamilton-Jacobi-like equations.Item Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework(1988) Cockburn, Bernardo; Shu, Chi-WangItem The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws IV: The Multidimensional Case(1989) Cockburn, Bernardo; Hou, Suchung; Shu, Chi-WangItem The Runge-Kutta Local Projection P1-Discontinuous-Galerkin Finite Element Method for Scalar Conservation Laws(1987) Cockburn, Bernardo; Shu, Chi-WangItem TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws III: One Dimensional Systems(1988) Cockburn, Bernardo; Lin, San-Yih; Shu, Chi-WangItem TVD Properties of a Class of Modified Eno Schemes for Scalar Conservation Laws(1987) Shu, Chi-Wang