| Author | L. Krivodonova, J. E. Flaherty |
|---|---|
| Title | Error Estimation for Discontinuous Galerkin Solutions of Multidimensional Hyperbolic Problems |
| Year | 2001 |
| Journal | Advances in Computational Mechanics |
| Abstract | We analyze the discretization errors of discontinuous Galerkin solutions of steady two-dimensional hyperbolic conservation laws on unstructured meshes. We shoe that the leading term of the error on each element is a linear combination of orthogonal polynominals of degrees p and p+1. We further show that there is a strong superconvergence property at the outflow edge(s) of each element where the average discretization error converges as o(h exp 2p+1) compared to a global rate of O(h exp p+1). Our analyses apply to both linear and non-linear conservation laws with smooth solutions. We show how to use our theory to construct efficient and asymptocally exact a posteriori discretization error estimates and we apply some examples. |
| PDF File |  Download |