{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T05:44:15Z","timestamp":1776836655813,"version":"3.51.2"},"reference-count":27,"publisher":"American Mathematical Society (AMS)","issue":"341","license":[{"start":{"date-parts":[[2024,1,27]],"date-time":"2024-01-27T00:00:00Z","timestamp":1706313600000},"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":["1912779"],"award-info":[{"award-number":["1912779"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["2208391"],"award-info":[{"award-number":["2208391"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1912779"],"award-info":[{"award-number":["1912779"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["2208391"],"award-info":[{"award-number":["2208391"]}],"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                    Structure-aware Taylor (SAT) methods are a class of timestepping schemes designed for propagating linear hyperbolic solutions within a tent-shaped spacetime region. Tents are useful to design explicit time marching schemes on unstructured advancing fronts with built-in locally variable timestepping for arbitrary spatial and temporal discretization orders. The main result of this paper is that an\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"s\">\n                        <mml:semantics>\n                          <mml:mi>s<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">s<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -stage SAT timestepping within a tent is weakly stable under the time step constraint\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"normal upper Delta t less-than-or-equal-to upper C h Superscript 1 plus 1 slash s\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi mathvariant=\"normal\">\n                              \u0394\n                              \n                            <\/mml:mi>\n                            <mml:mi>t<\/mml:mi>\n                            <mml:mo>\n                              \u2264\n                              \n                            <\/mml:mo>\n                            <mml:mi>C<\/mml:mi>\n                            <mml:msup>\n                              <mml:mi>h<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mn>1<\/mml:mn>\n                                <mml:mo>+<\/mml:mo>\n                                <mml:mn>1<\/mml:mn>\n                                <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                  <mml:mo>\/<\/mml:mo>\n                                <\/mml:mrow>\n                                <mml:mi>s<\/mml:mi>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\Delta t \\leq Ch^{1+1\/s}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , where\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"normal upper Delta t\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi mathvariant=\"normal\">\n                              \u0394\n                              \n                            <\/mml:mi>\n                            <mml:mi>t<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\Delta t<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is the time step size and\n                    <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>\n                    is the spatial mesh size. Improved stability properties are also presented for high-order SAT time discretizations coupled with low-order spatial polynomials. A numerical verification of the sharpness of proven estimates is also included.\n                  <\/p>","DOI":"10.1090\/mcom\/3811","type":"journal-article","created":{"date-parts":[[2022,12,14]],"date-time":"2022-12-14T11:42:16Z","timestamp":1671018136000},"page":"1061-1086","source":"Crossref","is-referenced-by-count":0,"title":["Stability of structure-aware Taylor methods for tents"],"prefix":"10.1090","volume":"92","author":[{"given":"Jay","family":"Gopalakrishnan","sequence":"first","affiliation":[]},{"given":"Zheng","family":"Sun","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2023,1,27]]},"reference":[{"key":"1","doi-asserted-by":"crossref","unstructured":"R. Abedi and R. B. Haber, Spacetime simulation of dynamic fracture with crack closure and frictional sliding, Adv. Model. Simul. Eng. 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