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ENO Multiresolution Schemes for General Discretizations

Reference Pascal Getreuer and François G. Meyer, “ENO Multiresolution Schemes for General Discretizations.” SIAM Journal on Numerical Analysis, vol. 46, no. 6, pp. 2953–2977, 2008. DOI: 10.1137/060663763.
Permalink http://dx.doi.org/10.1137/060663763
Bibtex
@article{getreuer08eno,
    title = {ENO Multiresolution Schemes for General Discretizations},
    author = {Pascal Getreuer and Fran\c{c}ois G. Meyer},
    journal = {SIAM Journal on Numerical Analysis},
    volume = {46},
    issue = {6},
    pages = {2953--2977},
    year = {2008},
    doi = {10.1137/060663763}
}

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Abstract
Harten’s framework is a nonlinear generalization of the wavelet framework. Previously, the choice of discretization (scaling function) in Harten multiresolution schemes has been limited to point-value, cell-average, and hat-based discretization. This paper shows how to construct multiresolution schemes consistent with Harten’s framework for a variety of discretizations. The construction here begins with the discrete operators and deduces the corresponding continuous operators, reversing the order of the usual approach. This construction yields as a special case essentially nonoscillatory (ENO) multiresolution schemes for any order of spline discretization and also has the flexibility to define multiresolution schemes with nonspline discretizations. An error-control strategy is also developed.

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