A posteriori error analysis of the discontinuous finite element methods for first order hyperbolic problems (Q654644)

The authors propose an a posteriori error analysis method for discontinuous Galerkin finite element approximations (DG) for steady and nonsteady first-order hyperbolic scale equations. Several residual-based a posteriori error estimators for the steady problem are constructed that provide global upper bounds on the error in DG-, \(L_2\)- and \(H^{-1}\)-norms, and local lower bounds on the error in \(L_2\)-norm. For the nonsteady problem the authors discretize the problem by employing an implicit Euler time scheme with space DG. The derived a posteriori error estimators yield the global upper bound on the error in \(L_\infty(0,T;L_2)\).