An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation
Mathematics of Computation
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Journal of Scientific Computing
Robust A Posteriori Error Estimates for Stationary Convection-Diffusion Equations
SIAM Journal on Numerical Analysis
Journal of Scientific Computing
deal.II—A general-purpose object-oriented finite element library
ACM Transactions on Mathematical Software (TOMS)
Journal of Computational and Applied Mathematics
Benchmark results for testing adaptive finite element eigenvalue procedures
Applied Numerical Mathematics
Computers & Mathematics with Applications
Computational Optimization and Applications
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A robust a-posteriori error estimator for interior penalty discontinuous Galerkin discretizations of a stationary convection-diffusion equation is derived. The estimator yields global upper and lower bounds of the error measured in terms of the energy norm and a semi-norm associated with the convective term in the equation. The ratio of the upper and lower bounds is independent of the magnitude of the Peclet number of the problem, and hence the estimator is fully robust for convection-dominated problems. Numerical examples are presented that illustrate the robustness and practical performance of the proposed error estimator in an adaptive refinement strategy.