Asymptotically exact a posteriori error estimates for a one-dimensional linear hyperbolic problem

Authors:
Slimane Adjerid;Mahboub Baccouch
Affiliations:
Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, United States;Department of Mathematics, University of Nebraska at Omaha, Omaha, NE 68182, United States
Venue:
Applied Numerical Mathematics
Year:
2010

Citing 7
Cited 3

Error estimates for finite element methods for scalar conservation laws

SIAM Journal on Numerical Analysis
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems

SIAM Journal on Numerical Analysis
Adaptive Discontinuous Galerkin Finite Element Methods for Nonlinear Hyperbolic Conservation Laws

SIAM Journal on Scientific Computing
Superconvergence of Discontinuous Finite Element Solutions for Transient Convection--diffusion Problems

Journal of Scientific Computing
The Discontinuous Galerkin Method for Two-Dimensional Hyperbolic Problems. Part I: Superconvergence Error Analysis

Journal of Scientific Computing
The Discontinuous Galerkin Method for Two-dimensional Hyperbolic Problems Part II: A Posteriori Error Estimation

Journal of Scientific Computing
Superconvergence of Discontinuous Galerkin and Local Discontinuous Galerkin Schemes for Linear Hyperbolic and Convection-Diffusion Equations in One Space Dimension

SIAM Journal on Numerical Analysis

Negative-Order Norm Estimates for Nonlinear Hyperbolic Conservation Laws

Journal of Scientific Computing
Asymptotically exact discontinuous Galerkin error estimates for linear symmetric hyperbolic systems

Applied Numerical Mathematics
Superconvergence and a posteriori error estimates for the LDG method for convection-diffusion problems in one space dimension

Computers & Mathematics with Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this manuscript we investigate the global convergence of the implicit residual-based a posteriori error estimates of Adjerid et al. (2002) [3]. The authors used the discontinuous Galerkin method to solve one-dimensional transient hyperbolic problems and showed that the local error on each element is proportional to a Radau polynomial. The discontinuous Galerkin error estimates under investigation are computed by solving a local steady problem on each element. Here we prove that, for smooth solutions, these a posteriori error estimates at a fixed time t converge to the true spatial error in the L^2 norm under mesh refinement.