Optimal Error Estimates of the Semidiscrete Central Discontinuous Galerkin Methods for Linear Hyperbolic Equations

2018/01/01 by Yong Liu, Chi-Wang Shu, Chi‐Wang Shu +1 · 1 citation
Engineering · Mathematics · #Computational Fluid Dynamics and Aerodynamics #Advanced Numerical Methods in Computational Mathematics #Numerical methods for differential equations

paper · doi:10.1137/16m1089484

Abstract

We analyze the central discontinuous Galerkin method for time-dependent linear conservation laws. In one dimension, optimal a priori L² error estimates of order k+1 are obtained for the semidiscrete scheme when piecewise polynomials of degree at most k (k≥0) 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.

Citations

• Error Estimates to Smooth Solutions of Runge--Kutta Discontinuous Galerkin Methods for Scalar Conservation Laws
• Strong Stability-Preserving High-Order Time Discretization Methods

Cited by

• Sub-optimal convergence of discontinuous Galerkin methods with central fluxes for linear hyperbolic equations with even degree polynomial approximations

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