| Abstrakt: |
Abstract: We consider the original DG method for solving the advection-reaction equations with arbitrary velocity in d space dimensions. For triangulations satisfying the flow condition, we first prove that the optimal convergence rate is of order k+1 in the L_2-norm if the method uses polynomials of order k. Then, a very simple derivative recovery formula is given to produce an approximation to the derivative in the flow direction which superconverges with order k+1. Further we consider a residual-based a posteriori error estimate and give the global upper bound and local lower bound on the error in the DG-norm, which is stronger than the L_2-norm. The key elements in our a posteriori analysis are the saturation assumption and an interpolation estimate between the DG spaces. We show that the a posteriori error bounds are efficient and reliable. Finally, some numerical experiments are presented to illustrate the theoretical analysis. |
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