{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T06:56:33Z","timestamp":1776840993267,"version":"3.51.2"},"reference-count":58,"publisher":"American Mathematical Society (AMS)","issue":"358","license":[{"start":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T00:00:00Z","timestamp":1772236800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"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                    We prove the stability and convergence of the high order discontinuous Galerkin scheme to spherically symmetric Einstein-scalar equations for a class of large initial data that ensures the formation of a black hole. Having chosen the Bondi coordinate system, we achieve\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L squared\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>L<\/mml:mi>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">L^2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    stability and obtain the optimal error estimates.\n                  <\/p>","DOI":"10.1090\/mcom\/4077","type":"journal-article","created":{"date-parts":[[2025,2,5]],"date-time":"2025-02-05T11:07:36Z","timestamp":1738753656000},"page":"557-587","source":"Crossref","is-referenced-by-count":0,"title":["On the convergence of the discontinuous Galerkin scheme for Einstein-scalar equations"],"prefix":"10.1090","volume":"95","author":[{"given":"Yuewen","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chi-Wang","family":"Shu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shing-Tung","family":"Yau","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2025,2,28]]},"reference":[{"issue":"4","key":"1","doi-asserted-by":"publisher","first-page":"2059","DOI":"10.1103\/PhysRevD.52.2059","article-title":"Three-dimensional numerical relativity: the evolution of black holes","volume":"52","author":"Anninos, Peter","year":"1995","journal-title":"Phys. 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