On the order of convergence of the discontinuous Galerkin method for hyperbolic equations
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- by Gerard R. Richter PDF
- Math. Comp. 77 (2008), 1871-1885 Request permission
Abstract:
The basic error estimate for the discontinuous Galerkin method for hyperbolic equations indicates an $O(h^{n+\frac {1}{2}})$ convergence rate for $n\textrm {th}$ degree polynomial approximation over a triangular mesh of size $h$. However, the optimal $O(h^{n+1})$ rate is frequently seen in practice. Here we extend the class of meshes for which sharpness of the $O(h^{n+\frac {1}{2}})$ estimate can be demonstrated, using as an example a problem with a “nonaligned” mesh in which all triangle sides are bounded away from the characteristic direction. The key to realizing $h^{n+\frac {1}{2}}$ convergence is a mesh which, to the extent possible, directs the error to lower frequency modes which are approximated, not damped, as $h\rightarrow 0$.References
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Additional Information
- Gerard R. Richter
- Affiliation: Department of Computer Science, Rutgers University, Busch Campus, Piscataway New Jersey 08854-8019
- Email: richter@cs.rutgers.edu
- Received by editor(s): February 15, 2007
- Received by editor(s) in revised form: November 20, 2007
- Published electronically: May 8, 2008
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 77 (2008), 1871-1885
- MSC (2000): Primary 65M60, 65M15
- DOI: https://doi.org/10.1090/S0025-5718-08-02126-1
- MathSciNet review: 2429867