Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations

Mar, 1984
Published in:
  • J.Comput.Phys. 53 (1984) 484

Citations per year

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Abstract: (Elsevier)
An adaptive method based on the idea of multiple component grids for the solution of hyperbolic partial differential equations using finite difference techniques is presented. Based upon Richardson-type estimates of the truncation error, refined grids are created or existing ones removed to attain a given accuracy for a minimum amount of work. The approach is recursive in that fine grids can contain even finer grids. The grids with finer mesh width in space also have a smaller mesh width in time, making this a mesh refinement algorithm in time and space. We present the algorithm, error estimation procedure, and the data structures, and conclude with numerical examples in one and two space dimensions.
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