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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.

Article permalink: http://dx.doi.org/10.1137/060663763

    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}


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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