## Fully adaptive multiresolution finite volume schemes for conservation laws (2003)

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Venue: | Math. Comp |

Citations: | 42 - 14 self |

### BibTeX

@ARTICLE{Cohen03fullyadaptive,

author = {Albert Cohen and Sidi Mahmoud Kaber and Siegfried Müller and Marie Postel},

title = {Fully adaptive multiresolution finite volume schemes for conservation laws},

journal = {Math. Comp},

year = {2003},

volume = {72},

pages = {2003}

}

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### Abstract

Abstract. 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. 1.

### Citations

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Citation Context ...tegy was initially developed for one-dimensional structured grids, several contributions have made it operational for various types of multivariate finite volume meshes (Cartesian [5, 8], curvilinear =-=[16, 30]-=-, triangular [13, 31] and unstructured [1]). Several remarks should be made concerning such a strategy: • The goal is not to improve the accuracy but rather to gain computational time while staying wi... |

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Citation Context ...s also interesting to note that, in contrast to Harten’s approach, the savings can be very effective in the context of a low order finite volume scheme. A first algorithm of this type was proposed in =-=[20]-=-, and is currently being tested for 2D problems with tensor product type discretizations ands186 A. COHEN, S. M. KABER, S. MÜLLER, AND M. POSTEL parametric patches to adapt the geometry of the domain.... |

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Finite volume schemes on triangles coupled with multiresolution analysis
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Citation Context ... ΨJ,λ =Ψj,k is explicitly defined by (33) Ψj,k = P J−1 J P J−2 J−1 j ···Pj+1 (0, ···,0, 1, −1, 0, ···, 0), with 1 at position 2k and −1 at position 2k +1,orequivalentlybyΨj,k := Φj,2k − Φj,2k+1,where =-=(34)-=- Φj,k = P J−1 J P J−2 J−1 j ···Pj+1 (0, ···,0, 1, 0, ···, 0), with 1 at position k. We are thus interested in the stability of the iterative applications of the prediction operators P j−1 j . This pro... |

2 | The h-p version of the element method for domains with curved boundaries - BABUSKA, GUO - 1988 |

2 | Adaptive volume schemes for conservation laws based on local multiresolution techniques - Gottschlich-Muller, Muller - 1998 |

1 |
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1 | Stationary subdivision, Memoirs of AMS 453 - Cavaretta, Dahmen, et al. - 1991 |

1 | Multiresolution volume schemes on triangles, preprint LAN Universite - Cohen, Dyn, et al. - 1999 |