A Posteriori Error Estimation for Adaptive Discontinuous Galerkin Approximations of Hyperbolic Systems
This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques, we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approximations of the exact error representation formula are then proposed and numerically evaluated for Ringleb flow, an exact solution of the 2-D Euler equations.
KeywordsPosteriori Error Discontinuous Galerkin Discontinuous Galerkin Method Dual Solution Posteriori Error Estimation
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