Discontinuous Galerkin via Interpolation: The Direct Flux Reconstruction Method
作者： H.T. Huynh
DOI: 10.2514/6.2019-3064
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摘要: The discontinuous Galerkin (DG) method is based on the idea of projection using integration. recent direct flux reconstruction (DFR) by Romero et al. (J Sci Comput 67(1):351–374, 2016) derived via interpolation and results in a scheme identical to DG (on hexahedral meshes). DFR further studied developed here. Two proofs for its equivalence with considerably simpler than original proof are presented. first employs $$ 2K - 1 degree precision K $$-point Gauss quadrature. second shows DG, FR, property that derivative + Lobatto polynomial vanishes at points. Fourier analysis these schemes presented an approach more geometric compared existing analytic approaches. effects nonuniform mesh those high-order transformation (a precursor curved meshes two three spatial dimensions) stability accuracy examined. These nonstandard analyses obtained in-depth study behavior eigenvalues eigenvectors.
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