Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Journal of Computational Physics
Parallel, adaptive finite element methods for conservation laws
Proceedings of the third ARO workshop on Adaptive methods for partial differential equations
On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Journal of Computational Physics
Weighted essentially non-oscillatory schemes on triangular meshes
Journal of Computational Physics
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Spectral (finite) volume method for conservation laws on unstructured grids: basic formulation
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Journal of Computational Physics
Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods
Journal of Computational Physics
Discontinuous Galerkin Methods Applied to Shock and Blast Problems
Journal of Scientific Computing
SIAM Journal on Scientific Computing
A p-multigrid discontinuous Galerkin method for the Euler equations on unstructured grids
Journal of Computational Physics
Spectral difference method for unstructured grids I: basic formulation
Journal of Computational Physics
SIAM Journal on Numerical Analysis
A central WENO scheme for solving hyperbolic conservation laws on non-uniform meshes
Journal of Computational Physics
Spatial and spectral superconvergence of discontinuous Galerkin method for hyperbolic problems
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Journal of Computational Physics
Very high order PNPM schemes on unstructured meshes for the resistive relativistic MHD equations
Journal of Computational Physics
ENO schemes with subcell resolution
Journal of Computational Physics
Journal of Computational Physics
Discontinuous Galerkin Methods: Theory, Computation and Applications
Discontinuous Galerkin Methods: Theory, Computation and Applications
A class of hybrid DG/FV methods for conservation laws II: Two-dimensional cases
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.46 |
By comparing the discontinuous Galerkin (DG) and the finite volume (FV) methods, a concept of 'static reconstruction' and 'dynamic reconstruction' is introduced for high-order numerical methods. Based on the new concept, a class of hybrid DG/FV schemes is presented for one-dimensional conservation law using a 'hybrid reconstruction' approach. In the hybrid DG/FV schemes, the lower-order derivatives of a piecewise polynomial solution are computed locally in a cell by the DG method based on Taylor basis functions (called as 'dynamic reconstruction'), while the higher-order derivatives are re-constructed by the 'static reconstruction' of the FV method, using the known lower-order derivatives in the cell itself and its adjacent neighboring cells. The hybrid DG/FV methods can greatly reduce CPU time and memory required by the traditional DG methods with the same order of accuracy on the same mesh, and they can be extended directly to unstructured and hybrid grids in two and three dimensions similar to the DG and/or FV methods. The hybrid DG/FV methods are applied to one-dimensional conservation law, including linear and non-linear scalar equation and Euler equations. In order to capture the strong shock waves without spurious oscillations, a simple shock detection approach is developed to mark 'trouble cells', and a moment limiter is adopted for higher-order schemes. The numerical results demonstrate the accuracy, and the super-convergence property is shown for the third-order hybrid DG/FV schemes. In addition, by analyzing the eigenvalues of the semi-discretized system in one dimension, we discuss the spectral properties of the hybrid DG/FV schemes to explain the super-convergence phenomenon.