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Spectral element approximation of convection-diffusion type problems. (English) Zbl 0964.65104
Summary: A spectral element implementation of the discontinuous Galerkin method is examined for convection-diffusion type problems. The computational domain is subdivided into non-overlapping subdomains, and a high-order, Legendre polynomial approximation is constructed on each subdomain. A variational formulation is used, and the flux across the subdomain interfaces is approximated using a van Leer flux splitting scheme for the convective terms and a penalty type method for the viscous terms.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
35Q53 KdV equations (Korteweg-de Vries equations)
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
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