| Author | SLIMANE ADJERID, KAREN D. DEVINE, JOSEPH E. FLAHERTY, LILIA KRIVODONOVA |
|---|---|
| Title | A POSTERIORI ERROR ESTIMATION FOR DISCONTINUOUS GALERKIN SOLUTIONS OF HYPERBOLIC PROBLEMS |
| Year | 2000 |
| Journal | Computer Method in Applied Mechanics and Engineering |
| Volume | - - |
| Pages | - - |
| Abstract | We analyze the spatial discretization errors associated with solutions of one- dimensional hyperbolic conservation laws by discontinuous Galerkin methods in space. We show that the leading term of the spatial discretization error with piece- wise polynomial approximations of degree p is proportional to a Radau polynomial of degree p+1 on each element. We also prove that the local and global discretiza- tion errors are O(x 2(p+1)) and O(x 2p+1) at the downwind point of each element. This strong superconvergence enables us to show that local and global discretiza- tion errors converge as O(x p+2) at the remaining roots of Radau polynomial of degree p+1 on each element. Convergence of local and global discretization errors to the Radau polynomial of degree p+1 also holds for smooth solutions as p!1. These results are used to construct asymptotically correct a posteriori estimates of spatial discretization errors that are effective for linear and nonlinear conservation laws in regions where solutions are smooth. |
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