{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T06:39:45Z","timestamp":1776839985256,"version":"3.51.2"},"reference-count":49,"publisher":"American Mathematical Society (AMS)","issue":"354","license":[{"start":{"date-parts":[[2025,9,6]],"date-time":"2025-09-06T00:00:00Z","timestamp":1757116800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["DMS-2309249"],"award-info":[{"award-number":["DMS-2309249"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004739","name":"Youth Innovation Promotion Association of the Chinese Academy of Sciences","doi-asserted-by":"publisher","award":["DMS-2309249"],"award-info":[{"award-number":["DMS-2309249"]}],"id":[{"id":"10.13039\/501100004739","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-2309249"],"award-info":[{"award-number":["DMS-2309249"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    In this paper, we propose a local discontinuous Galerkin (LDG) method for the Novikov equation that contains cubic nonlinear high-order derivatives. Flux correction techniques are used to ensure the stability of the numerical scheme. The\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper H Superscript 1\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>H<\/mml:mi>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">H^1<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -norm stability of the general solution and the error estimate for smooth solutions without using any priori assumptions are presented. Numerical examples demonstrate the accuracy and capability of the LDG method for solving the Novikov equation.\n                  <\/p>","DOI":"10.1090\/mcom\/4018","type":"journal-article","created":{"date-parts":[[2024,8,28]],"date-time":"2024-08-28T09:51:33Z","timestamp":1724838693000},"page":"1603-1631","source":"Crossref","is-referenced-by-count":1,"title":["A local discontinuous Galerkin method for the Novikov equation"],"prefix":"10.1090","volume":"94","author":[{"given":"Qi","family":"Tao","sequence":"first","affiliation":[]},{"given":"Xiang-Ke","family":"Chang","sequence":"additional","affiliation":[]},{"given":"Yong","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Chi-Wang","family":"Shu","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2024,9,6]]},"reference":[{"issue":"2","key":"1","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1006\/aima.1999.1883","article-title":"Multipeakons and the classical moment problem","volume":"154","author":"Beals, Richard","year":"2000","journal-title":"Adv. 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