An Analysis of the Discontinuous Galerkin Method for a Scalar Hyperbolic Equation
- 1 January 1986
- journal article
- Published by JSTOR in Mathematics of Computation
- Vol. 46 (173) , 1-26
- https://doi.org/10.2307/2008211
Abstract
We prove stability and error estimates for the discontinuous Galerkin method when applied to a scalar linear hyperbolic equation on a convex polygonal plane domain. Using finite element analysis techniques, we obtain estimates that are valid on an arbitrary locally regular triangulation of the domain and for an arbitrary degree of polynomials. estimates for are restricted to either a uniform or piecewise uniform triangulation and to polynomials of not higher than first degree. The latter estimates are proved by combining finite difference and finite element analysis techniques.Keywords
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