Abstract
In this paper we investigate the superconvergence properties of the discontinuous Galerkin method applied to scalar first-order hyperbolic partial differential equations on triangular meshes. We show that the discontinuous finite element solution is O(h p+2) superconvergent at the Legendre points on the outflow edge for triangles having one outflow edge. For triangles having two outflow edges the finite element error is O(h p+2) superconvergent at the end points of the inflow edge. Several numerical simulations are performed to validate the theory. In Part II of this work we explicitly write down a basis for the leading term of the error and construct asymptotically correct a posteriori error estimates by solving local hyperbolic problems with no boundary conditions on more general meshes.
Original language | English (US) |
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Pages (from-to) | 75-113 |
Number of pages | 39 |
Journal | Journal of Scientific Computing |
Volume | 33 |
Issue number | 1 |
DOIs | |
State | Published - Oct 2007 |
Externally published | Yes |
Keywords
- Discontinuous Galerkin method
- Hyperbolic problems
- Superconvergence
- Triangular meshes
ASJC Scopus subject areas
- Software
- Theoretical Computer Science
- Numerical Analysis
- Engineering(all)
- Computational Theory and Mathematics
- Computational Mathematics
- Applied Mathematics