TY - JOUR
T1 - Adaptive mesh refinement for hyperbolic partial differential equations
AU - Berger, Marsha J.
AU - Oliger, Joseph
N1 - Funding Information:
* This research was supported in part by Offtce of Naval Research Contract in part by National Science Foundation Grant MCS77-02082.
Funding Information:
We thank William Gropp for many helpful discussions, and for providing much of the graphical output for this paper. Computer time for this work was provided by the Stanford Linear Accelerator Center for the U.S. Department of Energy.
PY - 1984/3
Y1 - 1984/3
N2 - 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.
AB - 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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U2 - 10.1016/0021-9991(84)90073-1
DO - 10.1016/0021-9991(84)90073-1
M3 - Article
AN - SCOPUS:48749141209
SN - 0021-9991
VL - 53
SP - 484
EP - 512
JO - Journal of Computational Physics
JF - Journal of Computational Physics
IS - 3
ER -