An adaptive mesh redistribution method for nonlinear Hamilton--Jacobi equations in two-and three-dimensions

  • Authors:

  • H.-Z. Tang;Tao Tang;Pingwen Zhang

  • Affiliations:

  • School of Mathematical Sciences, Peking University, Beijing 100871, People's Republic of China;Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong and Institute of Computational Mathematics, The Chinese Academy of Sciences, Beijing 100080, People's Republic of C ...;School of Mathematical Sciences, Peking University, Beijing 100871, People's Republic of China

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2003

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Abstract

This paper presents an adaptive mesh redistribution (AMR) method for solving the nonlinear Hamilton-Jacobi equations and level-set equations in two- and three-dimensions. Our approach includes two key ingredients: a nonconservative second-order interpolation on the updated adaptive grids, and a class of monitor functions (or indicators) suitable for the Hamilton-Jacobi problems. The proposed adaptive mesh methods transform a uniform mesh in the logical domain to cluster grid points at the regions of the physical domain where the solution or its derivative is singular or nearly singular. Moreover, the formal second-order rate of convergence is preserved for the proposed AMR methods. Extensive numerical experiments are performed to demonstrate the efficiency and robustness of the proposed adaptive mesh algorithm.