A smoothness indicator for adaptive algorithms for hyperbolic systems
Journal of Computational Physics
An adaptive multiscale finite volume solver for unsteady and steady state flow computations
Journal of Computational Physics
Fully Adaptive Multiscale Schemes for Conservation Laws Employing Locally Varying Time Stepping
Journal of Scientific Computing
Error-control vs classical multiresolution algorithms for image compression
ISPRA'06 Proceedings of the 5th WSEAS International Conference on Signal Processing, Robotics and Automation
Detection, measurement and classification of discontinuities
ISPRA'06 Proceedings of the 5th WSEAS International Conference on Signal Processing, Robotics and Automation
ENO adaptive method for solving one-dimensional conservation laws
Applied Numerical Mathematics
Proceedings of the 7th international conference on Curves and Surfaces
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In this paper we describe and analyze a class of nonlinear \mr schemes for the multiresolution setting which corresponds to discretization by local averages with respect to the hat function. These schemes are based on the essentially-non-oscillatory (ENO) interpolatory procedure described in [A. Harten, B. Engquist, S. Osher, and S. Chakravarthy, J. Comput. Phys., 71 (1987), pp. 231--302]. We show that by allowing the approximation to fit the local nature of the data, one can improve the compression capabilities of the multiresolution algorithms. The question of stability for nonlinear (data-dependent) reconstruction techniques is also addressed.