Provably Stable Flux Reconstruction High-Order Methods on Curvilinear Elements
Alexander Cicchino,
David C. Del Rey Fernández,
Siva Nadarajah
et al.
Abstract:Provably stable flux reconstruction (FR) schemes are derived for partial differential equations cast in curvilinear coordinates. Specifically, energy stable flux reconstruction (ESFR) schemes are considered as they allow for design flexibility as well as stability proofs for the linear advection problem on affine elements.Additionally, split forms are examined as they enable the development of energy stability proofs. The first critical step proves, that in curvilinear coordinates, the discontinuous Galerkin (… Show more
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