{"id":{"repo_id":"heid-diss","oai_identifier":"oai:archiv.ub.uni-heidelberg.de:3992"},"canonical_url":"https://search.dev.ndltd.org/etd/heid-diss/oai:archiv.ub.uni-heidelberg.de:3992","repository":{"repo_id":"heid-diss","name":"Universität Heidelberg","base_url":"http://archiv.ub.uni-heidelberg.de/volltextserver/cgi/oai2"},"display":{"title":"A posteriori Error Estimators based on Duality Techniques from the Calculus of Variations","abstract":"A theoretical framework is presented within which we can systematically develop a posteriori error estimators for a quite general class of variational statements, involving a linear operator and two convex functionals. We merely require, that the linear operator be coercive and the corresponding functional be uniformly convex. As the second functional may be arbitrary, the theory can also cover constrained variational formulations. Two applications are discussed in detail: the Dirichlet Problem and the Obstacle Problem. A number of technical issues is considered, which pertain to the evaluation of the proposed error bounds using finite element methods: Inter alia a novel non-conforming discretisation scheme for the dual formulation is analysed. The resulting algebraic problem may be solved by a new preconditioned relaxation method, for which a proof of convergence is supplied.","abstract_html":"A theoretical framework is presented within which we can systematically develop a posteriori error estimators for a quite general class of variational statements, involving a linear operator and two convex functionals. We merely require, that the linear operator be coercive and the corresponding functional be uniformly convex. As the second functional may be arbitrary, the theory can also cover constrained variational formulations. Two applications are discussed in detail: the Dirichlet Problem and the Obstacle Problem. A number of technical issues is considered, which pertain to the evaluation of the proposed error bounds using finite element methods: Inter alia a novel non-conforming discretisation scheme for the dual formulation is analysed. The resulting algebraic problem may be solved by a new preconditioned relaxation method, for which a proof of convergence is supplied.","abstract_has_math":false,"creators":["Buß, Hinderk Martens"],"institution":"Universität Heidelberg","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Rannacher, Rolf"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2003,"date_issued":"2003-10-09","date_published":"2003-10-09","updated_at":"2026-07-24T02:29:42Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://www.ub.uni-heidelberg.de/archiv/3992","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Rannacher, Rolf"]},{"key":"dc:creator","label":"Author","values":["Buß, Hinderk Martens"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Universitätsbibliothek Heidelberg"]},{"key":"dc:type","label":"Dc Type","values":["doctoralThesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["thesis.doctoral"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Universität Heidelberg"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A theoretical framework is presented within which we can systematically develop a posteriori error estimators for a quite general class of variational statements, involving a linear operator and two convex functionals. We merely require, that the linear operator be coercive and the corresponding functional be uniformly convex. As the second functional may be arbitrary, the theory can also cover constrained variational formulations. Two applications are discussed in detail: the Dirichlet Problem and the Obstacle Problem. A number of technical issues is considered, which pertain to the evaluation of the proposed error bounds using finite element methods: Inter alia a novel non-conforming discretisation scheme for the dual formulation is analysed. The resulting algebraic problem may be solved by a new preconditioned relaxation method, for which a proof of convergence is supplied.","Ein allgemeiner theoretischer Rahmen wird entworfen, der die systematische Entwicklung von a posteriori Fehlerschätzern für Variationsprobleme eines relativ allgemeinen Typus ermöglicht: Zwei konvexe Funktionale sowie ein linearer Operator sind involviert. Vorausgesetzt wird neben der Koerzivität des linearen Operators lediglich die uniforme Konvexität des korrespondierenden Funktionals. Da das zweite Funktional beliebig gewählt werden darf, lassen sich auch restringierte Variationsprobleme betrachten. Anwendungen der Theorie werden in Gestalt des Dirichlet- und des Hindernis-Problems diskutiert. Es werden zudem praktische Fragen erörtert, die mit der Auswertung der Fehlerschätzer im Rahmen einer FEM-Simulation zusammenhängen: u. a. wird eine nicht-konforme Diskretisierungsmethode für die duale Formulierung vorgestellt und ein Konvergenzbeweis für ein neues präkonditioniertes Relaxationsverfahren angegeben, mit dessen Hilfe sich das diskretisierte Problem lösen läßt"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["A posteriori Error Estimators based on Duality Techniques from the Calculus of Variations","Über a posteriori Fehlerschätzer, die auf Dualitätsprinzipien der Variationsrechnung beruhen"]}]}],"canonical_facts":{"dc:contributor":["Rannacher, Rolf"],"dc:creator":["Buß, Hinderk Martens"],"dc:description.abstract":["A theoretical framework is presented within which we can systematically develop a posteriori error estimators for a quite general class of variational statements, involving a linear operator and two convex functionals. We merely require, that the linear operator be coercive and the corresponding functional be uniformly convex. As the second functional may be arbitrary, the theory can also cover constrained variational formulations. Two applications are discussed in detail: the Dirichlet Problem and the Obstacle Problem. A number of technical issues is considered, which pertain to the evaluation of the proposed error bounds using finite element methods: Inter alia a novel non-conforming discretisation scheme for the dual formulation is analysed. The resulting algebraic problem may be solved by a new preconditioned relaxation method, for which a proof of convergence is supplied.","Ein allgemeiner theoretischer Rahmen wird entworfen, der die systematische Entwicklung von a posteriori Fehlerschätzern für Variationsprobleme eines relativ allgemeinen Typus ermöglicht: Zwei konvexe Funktionale sowie ein linearer Operator sind involviert. Vorausgesetzt wird neben der Koerzivität des linearen Operators lediglich die uniforme Konvexität des korrespondierenden Funktionals. Da das zweite Funktional beliebig gewählt werden darf, lassen sich auch restringierte Variationsprobleme betrachten. Anwendungen der Theorie werden in Gestalt des Dirichlet- und des Hindernis-Problems diskutiert. Es werden zudem praktische Fragen erörtert, die mit der Auswertung der Fehlerschätzer im Rahmen einer FEM-Simulation zusammenhängen: u. a. wird eine nicht-konforme Diskretisierungsmethode für die duale Formulierung vorgestellt und ein Konvergenzbeweis für ein neues präkonditioniertes Relaxationsverfahren angegeben, mit dessen Hilfe sich das diskretisierte Problem lösen läßt"],"dc:format.medium":["application/pdf"],"dc:publisher":["Universitätsbibliothek Heidelberg"],"dc:title":["A posteriori Error Estimators based on Duality Techniques from the Calculus of Variations","Über a posteriori Fehlerschätzer, die auf Dualitätsprinzipien der Variationsrechnung beruhen"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Universität Heidelberg"]},"updated_at":"2026-07-24T02:29:42Z"}