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Third and Fourth Order Weighted ENO Schemes for Hamilton-Jacobi Equations on 2D Unstructured Meshes

In: Hyperbolic Problems: Theory, Numerics, Applications

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  • Yong-Tao Zhang

    (Brown University, Division of Applied Mathematics)

  • Chi-Wang Shu

    (Brown University, Division of Applied Mathematics)

Abstract

We present our recent work on designing third and fourth order accurate weighted essentially non-oscillatory (WENO) schemes for solving the nonlinear Hamilton-Jacobi equations on two-dimensional unstructured meshes. The main ideas are nodal based approximations, the usage of monotone Hamiltonians as building blocks on unstructured meshes, nonlinear weights using smooth indicators of second and higher derivatives, and a strategy to choose diversified smaller stencils to make up the bigger stencil in the WENO procedure. Both third-order and fourth-order WENO schemes use combinations of second-order approximations with nonlinear weights. A brief introduction to the methods and a selected few numerical experiments are included here.

Suggested Citation

  • Yong-Tao Zhang & Chi-Wang Shu, 2003. "Third and Fourth Order Weighted ENO Schemes for Hamilton-Jacobi Equations on 2D Unstructured Meshes," Springer Books, in: Thomas Y. Hou & Eitan Tadmor (ed.), Hyperbolic Problems: Theory, Numerics, Applications, pages 941-950, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-55711-8_89
    DOI: 10.1007/978-3-642-55711-8_89
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