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Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method: One-dimensional case. (English) Zbl 1039.65068
The authors introduce a weighted essentially nonoscillating (WENO) discrete Galerkin method for conservation laws in one spatial dimension. The method uses a Runge-Kutta scheme to propagate in time both the solution $$u$$ and the derivative $$\partial_x u$$. The construction of an approximate solution uses an Hermite interpolation of these values, together with a limitation of oscillations. Several example computations are given, comparing the method with more traditional WENO schemes.

##### MSC:
 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 65M20 Method of lines for initial value and initial-boundary value problems involving PDEs 35L65 Hyperbolic conservation laws
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