An energy stable approach for discretizing hyperbolic equations with nonconforming discontinuous Galerkin methods
Kozdon, Jeremy E.
Wilcox, Lucas C.
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When nonconforming, discontinuous Galerkin methods are implemented for hyperbolic equations using quadrature, exponential energy growth can result even when the underlying scheme with exact integration does not support such growth. Using linear elasticity as a model problem, we proposes a skew-symmetric formulation that has the same energy stability properties for both exact and inexact, quadrature-based integration. These stability properties are maintained even when the material properties are variable and discontinuous, and the elements non-affine (e.g., curved). The analytic stability results are confirmed through numerical experiments demonstrating the stability as well as the accuracy of the method.
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