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Preliminary results on the extension of eno schemes to two-dimensional problems

Numerical Analysis

Part of the Lecture Notes in Mathematics book series (LNM,volume 1270)

Abstract

In this paper we present preliminary results on the extension of high-order accurate essentially non-oscillatory (ENO) schemes to the solution of hyperbolic systems of conservation laws in 2D. The design involves an essentially non-oscillatory piecewise polynomial reconstruction of the solution from its cell averages, solution in the small of the resulting piecewise polynomial initial value problem, and averaging of this solution over each cell. Unlike standard finite difference methods this procedure uses an adaptive stencil of grid points and consequently the resulting schemes are highly nonlinear.

Keywords

  • Initial Value Problem
  • Level Curf
  • Spurious Oscillation
  • Piecewise Smooth Function
  • Periodic Initial Value Problem

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1987 Springer-Verlag

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Harten, A. (1987). Preliminary results on the extension of eno schemes to two-dimensional problems. In: Carasso, C., Serre, D., Raviart, PA. (eds) Nonlinear Hyperbolic Problems. Lecture Notes in Mathematics, vol 1270. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078315

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  • DOI: https://doi.org/10.1007/BFb0078315

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18200-9

  • Online ISBN: 978-3-540-47805-8

  • eBook Packages: Springer Book Archive