{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T02:52:20Z","timestamp":1776826340445,"version":"3.51.2"},"reference-count":32,"publisher":"American Mathematical Society (AMS)","issue":"222","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    The convergence of the discontinuous Galerkin method for the nonlinear (cubic) Schr\u00f6dinger equation is analyzed in this paper. We show the existence of the resulting approximations and prove optimal order error estimates in\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L Superscript normal infinity Baseline left-parenthesis upper L squared right-parenthesis period\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msup>\n                              <mml:mi>L<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi mathvariant=\"normal\">\n                                  \u221e\n                                  \n                                <\/mml:mi>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:msup>\n                              <mml:mi>L<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mn>2<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>.<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">L^{\\infty }(L^{2} ) .<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    These estimates are valid under weak restrictions on the space-time mesh.\n                  <\/p>","DOI":"10.1090\/s0025-5718-98-00946-6","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"479-499","source":"Crossref","is-referenced-by-count":129,"title":["A space-time finite element method for the nonlinear Schr\u00f6dinger equation: the discontinuous Galerkin method"],"prefix":"10.1090","volume":"67","author":[{"given":"Ohannes","family":"Karakashian","sequence":"first","affiliation":[]},{"given":"Charalambos","family":"Makridakis","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1998]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/BF01385769","article-title":"On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schr\u00f6dinger equation","volume":"59","author":"Akrivis, Georgios D.","year":"1991","journal-title":"Numer. 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