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Comp."],"abstract":"<p>\n                    We study semi-Lagrangian discontinuous Galerkin (SLDG) and Runge-Kutta discontinuous Galerkin (RKDG) schemes for some front propagation problems in the presence of an obstacle term, modeled by a nonlinear Hamilton-Jacobi equation of the form\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"min left-parenthesis u Subscript t Baseline plus c u Subscript x Baseline comma u minus g left-parenthesis x right-parenthesis right-parenthesis equals 0\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mo movablelimits=\"true\" form=\"prefix\">min<\/mml:mo>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:msub>\n                              <mml:mi>u<\/mml:mi>\n                              <mml:mi>t<\/mml:mi>\n                            <\/mml:msub>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:mi>c<\/mml:mi>\n                            <mml:msub>\n                              <mml:mi>u<\/mml:mi>\n                              <mml:mi>x<\/mml:mi>\n                            <\/mml:msub>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>u<\/mml:mi>\n                            <mml:mo>\n                              \u2212\n                              \n                            <\/mml:mo>\n                            <mml:mi>g<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>x<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\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\">\\min (u_t + c u_x, u - g(x))=0<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , in one space dimension. New convergence results and error bounds are obtained for Lipschitz regular data. These \u201clow regularity\u201d assumptions are the natural ones for the solutions of the studied equations. Numerical tests are given to illustrate the behavior of our schemes.\n                  <\/p>","DOI":"10.1090\/mcom\/3072","type":"journal-article","created":{"date-parts":[[2015,5,6]],"date-time":"2015-05-06T11:54:45Z","timestamp":1430913285000},"page":"2131-2159","source":"Crossref","is-referenced-by-count":3,"title":["Convergence of discontinuous Galerkin schemes for front propagation with obstacles"],"prefix":"10.1090","volume":"85","author":[{"given":"Olivier","family":"Bokanowski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yingda","family":"Cheng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chi-Wang","family":"Shu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2015,12,29]]},"reference":[{"issue":"12","key":"1","doi-asserted-by":"publisher","first-page":"1339","DOI":"10.1002\/(SICI)1097-0312(199612)49:12<1339::AID-CPA5>3.0.CO;2-B","article-title":"Numerical discretization of the first-order Hamilton-Jacobi equation on triangular meshes","volume":"49","author":"Abgrall, R.","year":"1996","journal-title":"Comm. 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