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Comp."],"abstract":"<p>\n                    As a first step towards time-stepping schemes for constrained PDE systems, this paper presents convergence results for the temporal discretization of operator DAEs. We consider linear, semi-explicit systems which include e.g. the Stokes equations or applications with boundary control. To guarantee unique approximations, we restrict the analysis to algebraically stable Runge-Kutta methods for which the stability functions satisfy\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper R left-parenthesis normal infinity right-parenthesis equals 0\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>R<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi mathvariant=\"normal\">\n                              \u221e\n                              \n                            <\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>0<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">R(\\infty )=0<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . As expected from the theory of DAEs, the convergence properties of the single variables differ and depend strongly on the assumed smoothness of the data.\n                  <\/p>","DOI":"10.1090\/mcom\/3270","type":"journal-article","created":{"date-parts":[[2017,3,22]],"date-time":"2017-03-22T10:01:12Z","timestamp":1490176872000},"page":"149-174","source":"Crossref","is-referenced-by-count":11,"title":["Runge-Kutta methods for linear semi-explicit operator differential-algebraic equations"],"prefix":"10.1090","volume":"87","author":[{"given":"R.","family":"Altmann","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"C.","family":"Zimmer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2017,6,21]]},"reference":[{"issue":"5","key":"1","doi-asserted-by":"publisher","first-page":"1489","DOI":"10.1051\/m2an\/2015029","article-title":"Finite element decomposition and minimal extension for flow equations","volume":"49","author":"Altmann, R.","year":"2015","journal-title":"ESAIM Math. 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