## The discontinuous Galerkin method with diffusion

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- by Gerard R. Richter PDF
- Math. Comp.
**58**(1992), 631-643 Request permission

## Abstract:

We propose a way of extending the discontinuous Galerkin method from pure hyperbolic equations to convection-dominated equations with an $O(h)$ diffusion term. The resulting method is explicit and can be applied with polynomials of degree $n \geq 1$. The extended method satisfies the same $O({h^{n + 1/2}})$ error estimate previously established for the discontinuous Galerkin method as applied to hyperbolic problems. Numerical results are provided.## References

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## Additional Information

- © Copyright 1992 American Mathematical Society
- Journal: Math. Comp.
**58**(1992), 631-643 - MSC: Primary 65M60; Secondary 65M15, 65N30, 76M25, 76Rxx
- DOI: https://doi.org/10.1090/S0025-5718-1992-1122076-2
- MathSciNet review: 1122076