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The local discontinuous Galerkin method for time-dependent convection-diffusion systems. (English) Zbl 0927.65118
The authors analyze the local discontinuous Galerkin methods for some nonlinear, time-dependent convection-diffusion systems. The nonlinear terms are considered such that compressible Navier-Stokes equations and the equations of the hydrodynamic model for semiconductor device simulation could be taken into account.
The analysis is sharp, with some preliminary numerical results in the one-dimensional case. The main conclusion underlines the high parallelizability of these methods which, by far, compensates for their extra amount of local computation.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
35Q30 Navier-Stokes equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65Y05 Parallel numerical computation
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