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Mathematics of Computation

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The discontinuous Galerkin method with diffusion

Author: Gerard R. Richter
Journal: Math. Comp. 58 (1992), 631-643
MSC: Primary 65M60; Secondary 65M15, 65N30, 76M25, 76Rxx
MathSciNet review: 1122076
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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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Keywords: Finite element, hyperbolic
Article copyright: © Copyright 1992 American Mathematical Society