{"id":{"repo_id":"freiburg-diss","oai_identifier":"oai:freidok.uni-freiburg.de:337"},"canonical_url":"https://search.dev.ndltd.org/etd/freiburg-diss/oai:freidok.uni-freiburg.de:337","repository":{"repo_id":"freiburg-diss","name":"University of Freiburg","base_url":"https://freidok.uni-freiburg.de/oai/oai2.php"},"display":{"title":"Error estimates for numerical approximations to scalar conservation laws","abstract":"In this thesis we are concerned with a-priori and a-posteriori error estimates <br>for certain finite volume approximations of scalar hyperbolic conservation laws. <br>We introduce a new technique to prove a-priori error estimates which is based <br>on a duality argument and involves a consistency error of cell averages. <br>Next, we generalize finite volume schemes on staggered grids to several <br>space dimensions and to a large class of unstructured grids. We give a <br>complete a priori and a posteriori error analysis. Furthermore, we study <br>higher order schemes and implicit schemes.","abstract_html":"In this thesis we are concerned with a-priori and a-posteriori error estimates &lt;br&gt;for certain finite volume approximations of scalar hyperbolic conservation laws. &lt;br&gt;We introduce a new technique to prove a-priori error estimates which is based &lt;br&gt;on a duality argument and involves a consistency error of cell averages. &lt;br&gt;Next, we generalize finite volume schemes on staggered grids to several &lt;br&gt;space dimensions and to a large class of unstructured grids. We give a &lt;br&gt;complete a priori and a posteriori error analysis. Furthermore, we study &lt;br&gt;higher order schemes and implicit schemes.","abstract_has_math":false,"creators":["Küther, Marc"],"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":"2026-07-24T02:21:35Z","subjects":["a-posteriori Fehlerabschätzung","a-priori Fehlerabschätzung","hyperbolische Differentialgleichung","error estimates","staggered grids","hyperbolic partial differential equation"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://freidok.uni-freiburg.de/data/337","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":["Küther, Marc"]}]},{"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":["a-posteriori Fehlerabschätzung","a-priori Fehlerabschätzung","hyperbolische Differentialgleichung","error estimates","staggered grids","hyperbolic partial differential equation"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis we are concerned with a-priori and a-posteriori error estimates <br>for certain finite volume approximations of scalar hyperbolic conservation laws. <br>We introduce a new technique to prove a-priori error estimates which is based <br>on a duality argument and involves a consistency error of cell averages. <br>Next, we generalize finite volume schemes on staggered grids to several <br>space dimensions and to a large class of unstructured grids. We give a <br>complete a priori and a posteriori error analysis. Furthermore, we study <br>higher order schemes and implicit schemes."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Error estimates for numerical approximations to scalar conservation laws","Fehlerabschätzungen für numerische Approximationen von skalaren Erhaltungsgleichungen"]}]}],"canonical_facts":{"dc:contributor":["Kröner, Dietmar"],"dc:creator":["Küther, Marc"],"dc:description.abstract":["In this thesis we are concerned with a-priori and a-posteriori error estimates <br>for certain finite volume approximations of scalar hyperbolic conservation laws. <br>We introduce a new technique to prove a-priori error estimates which is based <br>on a duality argument and involves a consistency error of cell averages. <br>Next, we generalize finite volume schemes on staggered grids to several <br>space dimensions and to a large class of unstructured grids. We give a <br>complete a priori and a posteriori error analysis. Furthermore, we study <br>higher order schemes and implicit schemes."],"dc:format.medium":["application/pdf"],"dc:subject":["a-posteriori Fehlerabschätzung","a-priori Fehlerabschätzung","hyperbolische Differentialgleichung","error estimates","staggered grids","hyperbolic partial differential equation"],"dc:title":["Error estimates for numerical approximations to scalar conservation laws","Fehlerabschätzungen für numerische Approximationen von skalaren Erhaltungsgleichungen"],"dc:type":["DoctoralThesis"]},"updated_at":"2026-07-24T02:21:35Z"}