2001/12/05 by Albert Cohen, Sidi Kaber, Sidi Mahmoud Kaber +2 · 203 citations
Earth and Planetary Sciences · Engineering · Mathematics · #Algorithm #Applied mathematics #Artificial intelligence #Computation #Computational Fluid Dynamics and Aerodynamics #Computer science #Conservation law #Context (archaeology) #Finite volume method #Fluid Dynamics and Turbulent Flows #Geometry #Grid #Mathematical analysis #Mathematical optimization #Mathematics #Meteorological Phenomena and Simulations #Multiresolution analysis
paper · pdf · doi:10.1090/s0025-5718-01-01391-6
published in Mathematics of Computation 72(241), 183-225 (American Mathematical Society)
openalex publication_date 2001/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
The use of multiresolution decompositions in the context of finite volume schemes for conservation laws was first proposed by A. Harten for the purpose of accelerating the evaluation of numerical fluxes through an adaptive computation. In this approach the solution is still represented at each time step on the finest grid, resulting in an inherent limitation of the potential gain in memory space and computational time. The present paper is concerned with the development and the numerical analysis of fully adaptive multiresolution schemes, in which the solution is represented and computed in a dynamically evolved adaptive grid. A crucial problem is then the accurate computation of the flux without the full knowledge of fine grid cell averages. Several solutions to this problem are proposed, analyzed, and compared in terms of accuracy and complexity.