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Comp."],"abstract":"<p>In this paper we introduce a general framework for defining and studying essentially nonoscillatory reconstruction procedures of arbitrarily high order of accuracy, interpolating data in the central stencil around a given computational cell (<inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"sans-serif upper C sans-serif upper W sans-serif upper E sans-serif upper N sans-serif upper O\">\n  <mml:semantics>\n    <mml:mrow class=\"MJX-TeXAtom-ORD\">\n      <mml:mi mathvariant=\"sans-serif\">C<\/mml:mi>\n      <mml:mi mathvariant=\"sans-serif\">W<\/mml:mi>\n      <mml:mi mathvariant=\"sans-serif\">E<\/mml:mi>\n      <mml:mi mathvariant=\"sans-serif\">N<\/mml:mi>\n      <mml:mi mathvariant=\"sans-serif\">O<\/mml:mi>\n    <\/mml:mrow>\n    <mml:annotation encoding=\"application\/x-tex\">\\mathsf {CWENO}<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula>). This technique relies on the same selection mechanism of smooth stencils adopted in <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"sans-serif upper W sans-serif upper E sans-serif upper N sans-serif upper O\">\n  <mml:semantics>\n    <mml:mrow class=\"MJX-TeXAtom-ORD\">\n      <mml:mi mathvariant=\"sans-serif\">W<\/mml:mi>\n      <mml:mi mathvariant=\"sans-serif\">E<\/mml:mi>\n      <mml:mi mathvariant=\"sans-serif\">N<\/mml:mi>\n      <mml:mi mathvariant=\"sans-serif\">O<\/mml:mi>\n    <\/mml:mrow>\n    <mml:annotation encoding=\"application\/x-tex\">\\mathsf {WENO}<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula>, but here the pool of candidates for the selection includes polynomials of different degrees. This seemingly minor difference allows us to compute the analytic expression of a polynomial interpolant, approximating the unknown function uniformly within a cell, instead of only at one point at a time. For this reason this technique is particularly suited for balance laws for finite volume schemes, when averages of source terms require high order quadrature rules based on several points; in the computation of local averages, during refinement in <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"h\">\n  <mml:semantics>\n    <mml:mi>h<\/mml:mi>\n    <mml:annotation encoding=\"application\/x-tex\">h<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula>-adaptive schemes; or in the transfer of the solution between grids in moving mesh techniques, and in general when a globally defined reconstruction is needed. Previously, these needs have been satisfied mostly by ENO reconstruction techniques, which, however, require a much wider stencil than the <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"sans-serif upper C sans-serif upper W sans-serif upper E sans-serif upper N sans-serif upper O\">\n  <mml:semantics>\n    <mml:mrow class=\"MJX-TeXAtom-ORD\">\n      <mml:mi mathvariant=\"sans-serif\">C<\/mml:mi>\n      <mml:mi mathvariant=\"sans-serif\">W<\/mml:mi>\n      <mml:mi mathvariant=\"sans-serif\">E<\/mml:mi>\n      <mml:mi mathvariant=\"sans-serif\">N<\/mml:mi>\n      <mml:mi mathvariant=\"sans-serif\">O<\/mml:mi>\n    <\/mml:mrow>\n    <mml:annotation encoding=\"application\/x-tex\">\\mathsf {CWENO}<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula> reconstruction studied here, for the same accuracy.<\/p>","DOI":"10.1090\/mcom\/3273","type":"journal-article","created":{"date-parts":[[2017,6,14]],"date-time":"2017-06-14T15:38:21Z","timestamp":1497454701000},"page":"1689-1719","source":"Crossref","is-referenced-by-count":84,"title":["CWENO: Uniformly accurate reconstructions for balance laws"],"prefix":"10.1090","volume":"87","author":[{"given":"I.","family":"Cravero","sequence":"first","affiliation":[]},{"given":"G.","family":"Puppo","sequence":"additional","affiliation":[]},{"given":"M.","family":"Semplice","sequence":"additional","affiliation":[]},{"given":"G.","family":"Visconti","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2017,11,2]]},"reference":[{"issue":"2","key":"1","doi-asserted-by":"publisher","first-page":"893","DOI":"10.1137\/100791579","article-title":"Analysis of WENO schemes for full and global accuracy","volume":"49","author":"Ar\u00e0ndiga, F.","year":"2011","journal-title":"SIAM J. 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