The discontinuous Galerkin method with diffusion

Richter, Gerard R.

doi:10.1090/S0025-5718-1992-1122076-2

The discontinuous Galerkin method with diffusion
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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.

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Triangular mesh methods for the neutron transport equation

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