{"id":{"repo_id":"freiburg-diss","oai_identifier":"oai:freidok.uni-freiburg.de:1284"},"canonical_url":"https://search.dev.ndltd.org/etd/freiburg-diss/oai:freidok.uni-freiburg.de:1284","repository":{"repo_id":"freiburg-diss","name":"University of Freiburg","base_url":"https://freidok.uni-freiburg.de/oai/oai2.php"},"display":{"title":"Finite volume schemes for hyperbolic-parabolic systems : error estimates","abstract":"Finite-volume schemes on unstructured grids are the most frequently used <br>to approximate solutions of systems of hyperbolic balance laws in multi-space dimension. <br>The convergence analysis for the scalar case is well developed, even though <br>not complete up to now. In contrast, very few is known for the case of systems. <br>Following the ideas of J.P. Vila and P. Villedieu on one side, and of C.Dafermos on the other side, we derive error estimates of the order $O(h^{1/2})$ for finite volume schemes to some hyperbolic--parabolic systems in multi-space dimension. This includes in particular the Euler system with a source term, the compressible Navier--Stokes system and the Friedrichs' system. The error estimates are valid for smooth solutions. In addition, in the case of the Friedrichs' system they hold also for solutions with jumps.","abstract_html":"Finite-volume schemes on unstructured grids are the most frequently used &lt;br&gt;to approximate solutions of systems of hyperbolic balance laws in multi-space dimension. &lt;br&gt;The convergence analysis for the scalar case is well developed, even though &lt;br&gt;not complete up to now. In contrast, very few is known for the case of systems. &lt;br&gt;Following the ideas of J.P. Vila and P. Villedieu on one side, and of C.Dafermos on the other side, we derive error estimates of the order <span class=\"etd-inline-math\">O(h<sup>1/2</sup>)</span> for finite volume schemes to some hyperbolic--parabolic systems in multi-space dimension. This includes in particular the Euler system with a source term, the compressible Navier--Stokes system and the Friedrichs&#x27; system. The error estimates are valid for smooth solutions. In addition, in the case of the Friedrichs&#x27; system they hold also for solutions with jumps.","abstract_has_math":true,"creators":["Jovanovic, Vladimir"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Kröner, Dietmar"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T02:22:10Z","subjects":["Finite Volumen Verfahren","Navier-Stokes System","Finite Volume Schemes","Balance Laws"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://freidok.uni-freiburg.de/data/1284","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Kröner, Dietmar"]},{"key":"dc:creator","label":"Author","values":["Jovanovic, Vladimir"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:type","label":"Dc Type","values":["DoctoralThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Finite Volumen Verfahren","Navier-Stokes System","Finite Volume Schemes","Balance Laws"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Finite-volume schemes on unstructured grids are the most frequently used <br>to approximate solutions of systems of hyperbolic balance laws in multi-space dimension. <br>The convergence analysis for the scalar case is well developed, even though <br>not complete up to now. In contrast, very few is known for the case of systems. <br>Following the ideas of J.P. Vila and P. Villedieu on one side, and of C.Dafermos on the other side, we derive error estimates of the order $O(h^{1/2})$ for finite volume schemes to some hyperbolic--parabolic systems in multi-space dimension. This includes in particular the Euler system with a source term, the compressible Navier--Stokes system and the Friedrichs' system. The error estimates are valid for smooth solutions. In addition, in the case of the Friedrichs' system they hold also for solutions with jumps.","Finite Volumen Verfahren auf unstrukturierten Gittern treten am häufigsten bei Approximieren von Erhaltungsgleichungen in mehreren Dimensionen auf. Die Analyse der Konvergenz im skalaren Fall hat wesentliche Ergebnisse erzielt, obwohl sie ihren endgültigen Stand noch nicht erreicht hat. Was es Systeme angeht, es ist nur wenig darüber bekannt. <br>In diesem Werk folgen wir einerseits die Ideen von J.P. Vila und P. Villedieu, <br>und anderseits die Ideen von C. Dafermos, um die Fehlerabschätzungen von der Ordnung $O(h^{1/2})$ für Finite Volumen Verfahren für gewisse hyperbolisch-- parabolische Systeme herzuleiten. Insbesondere betrachten wir das Euler System mit dem Quellenterm, das compressible Navier--Stokes System und das Friedrichs System. Die Fehlerabschätzungen gelten für glatte Lösungen. Darüber hinaus gelten sie auch für die Lösungen mit Sprüngen im Fall von dem Friedrichs System."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Finite volume schemes for hyperbolic-parabolic systems : error estimates","Finite Volumenverfahren für hyperbolisch-parabolische Systeme : Fehlerabschätzungen"]}]}],"canonical_facts":{"dc:contributor":["Kröner, Dietmar"],"dc:creator":["Jovanovic, Vladimir"],"dc:description.abstract":["Finite-volume schemes on unstructured grids are the most frequently used <br>to approximate solutions of systems of hyperbolic balance laws in multi-space dimension. <br>The convergence analysis for the scalar case is well developed, even though <br>not complete up to now. In contrast, very few is known for the case of systems. <br>Following the ideas of J.P. Vila and P. Villedieu on one side, and of C.Dafermos on the other side, we derive error estimates of the order $O(h^{1/2})$ for finite volume schemes to some hyperbolic--parabolic systems in multi-space dimension. This includes in particular the Euler system with a source term, the compressible Navier--Stokes system and the Friedrichs' system. The error estimates are valid for smooth solutions. In addition, in the case of the Friedrichs' system they hold also for solutions with jumps.","Finite Volumen Verfahren auf unstrukturierten Gittern treten am häufigsten bei Approximieren von Erhaltungsgleichungen in mehreren Dimensionen auf. Die Analyse der Konvergenz im skalaren Fall hat wesentliche Ergebnisse erzielt, obwohl sie ihren endgültigen Stand noch nicht erreicht hat. Was es Systeme angeht, es ist nur wenig darüber bekannt. <br>In diesem Werk folgen wir einerseits die Ideen von J.P. Vila und P. Villedieu, <br>und anderseits die Ideen von C. Dafermos, um die Fehlerabschätzungen von der Ordnung $O(h^{1/2})$ für Finite Volumen Verfahren für gewisse hyperbolisch-- parabolische Systeme herzuleiten. Insbesondere betrachten wir das Euler System mit dem Quellenterm, das compressible Navier--Stokes System und das Friedrichs System. Die Fehlerabschätzungen gelten für glatte Lösungen. Darüber hinaus gelten sie auch für die Lösungen mit Sprüngen im Fall von dem Friedrichs System."],"dc:format.medium":["application/pdf"],"dc:subject":["Finite Volumen Verfahren","Navier-Stokes System","Finite Volume Schemes","Balance Laws"],"dc:title":["Finite volume schemes for hyperbolic-parabolic systems : error estimates","Finite Volumenverfahren für hyperbolisch-parabolische Systeme : Fehlerabschätzungen"],"dc:type":["DoctoralThesis"]},"updated_at":"2026-07-24T02:22:10Z"}