Journal of Computational Physics
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
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
A Local Discontinuous Galerkin Method for KdV Type Equations
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Journal of Scientific Computing
Postprocessing for the Discontinuous Galerkin Method over Nonuniform Meshes
SIAM Journal on Scientific Computing
Superconvergence and time evolution of discontinuous Galerkin finite element solutions
Journal of Computational Physics
Superconvergence of Discontinuous Galerkin Methods for Convection-Diffusion Problems
Journal of Scientific Computing
LDG2: A Variant of the LDG Flux Formulation for the Spectral Volume Method
Journal of Scientific Computing
SIAM Journal on Numerical Analysis
Hi-index | 7.29 |
We study the superconvergence property of the local discontinuous Galerkin (LDG) method for solving the linearized Korteweg-de Vries (KdV) equation. We prove that, if the piecewise P^k polynomials with k=1 are used, the LDG solution converges to a particular projection of the exact solution with the order k+3/2, when the upwind flux is used for the convection term and the alternating flux is used for the dispersive term. Numerical examples are provided at the end to support the theoretical results.