M. Griebel and G. W. Zumbusch.
Adaptive sparse grids for hyperbolic conservation laws.
In M. Fey and R. Jeltsch, editors, Hyperbolic Problems: Theory,
Numerics, Applications. 7th International Conference in Zürich, February
1998, volume 1 of International Series of Numerical Mathematics 129,
pages 411-422, Basel, Switzerland, 1999. Birkhäuser.
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We report on numerical experiments using adaptive sparse grid discretization techniques for the numerical solution of scalar hyperbolic conservation laws. Sparse grids are an efficient approximation method for functions. Compared to regular, uniform grids of a mesh parameter h contain h-d points in d dimensions, sparse grids require only h-1|logh|d-1 points due to a truncated, tensor-product multi-scale basis representation.