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Entropy-stable, high-order summation-by-parts discretizations without interface penalties. (English) Zbl 1434.65184
The author combines nodal summation-by-parts operators as in continuous Galerkin methods to construct entropy conservative semidiscretizations of hyperbolic conservation laws. A local projection stabilization is used to reduce possible oscillations and render the scheme entropy dissipative. Numerical results for the linear advection and compressible Euler equations are presented.

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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