1. Optimal Error Estimates of the Semidiscrete Central Discontinuous Galerkin Methods for Linear Hyperbolic Equations
- Author
-
Yong Liu, Chi-Wang Shu, and Mengping Zhang
- Subjects
Numerical Analysis ,Conservation law ,Degree (graph theory) ,Applied Mathematics ,010103 numerical & computational mathematics ,01 natural sciences ,Mathematics::Numerical Analysis ,law.invention ,010101 applied mathematics ,Computational Mathematics ,Dimension (vector space) ,Discontinuous Galerkin method ,law ,Piecewise ,Applied mathematics ,Polygon mesh ,Cartesian coordinate system ,0101 mathematics ,Hyperbolic partial differential equation ,Mathematics - Abstract
We analyze the central discontinuous Galerkin method for time-dependent linear conservation laws. In one dimension, optimal a priori $L^2$ error estimates of order $k+1$ are obtained for the semidiscrete scheme when piecewise polynomials of degree at most $k$ ($k\geq0$) are used on overlapping uniform meshes. We then extend the analysis to multidimensions on uniform Cartesian meshes when piecewise tensor-product polynomials are used on overlapping meshes. Numerical experiments are given to demonstrate the theoretical results.
- Published
- 2018