Numerical Comparison of WENO Finite Volume and Runge–Kutta Discontinuous Galerkin Methods

  • Authors:

  • Tie Zhou;Yinfan Li;Chi-Wang Shu

  • Affiliations:

  • School of Mathematical Sciences, Peking University, Beijing 100871, People's Republic of China;Institute of Computational Mathematics, Academia Sinica, Beijing 100080, People's Republic of China;Division of Applied Mathematics, Brown University, Providence, RI 02912, USA. shu@cfm.brown.edu

  • Venue:
  • Journal of Scientific Computing
  • Year:
  • 2001

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Abstract

High order WENO (weighted essentially non-oscillatory) schemes and discontinuous Galerkin methods are two classes of high order, high resolution methods suitable for convection dominated simulations with possible discontinuous or sharp gradient solutions. In this paper we first review these two classes of methods, pointing out their similarities and differences in algorithm formulation, theoretical properties, implementation issues, applicability, and relative advantages. We then present some quantitative comparisons of the third order finite volume WENO methods and discontinuous Galerkin methods for a series of test problems to assess their relative merits in accuracy and CPU timing.