{"id":{"repo_id":"freiburg-diss","oai_identifier":"oai:freidok.uni-freiburg.de:178"},"canonical_url":"https://search.dev.ndltd.org/etd/freiburg-diss/oai:freidok.uni-freiburg.de:178","repository":{"repo_id":"freiburg-diss","name":"University of Freiburg","base_url":"https://freidok.uni-freiburg.de/oai/oai2.php"},"display":{"title":"A posteriori error estimates and adaptive methods for convection dominated transport processes","abstract":"In this thesis we derive robust a posteriori error estimates
for finite volume approximations of convection dominated nonlinear
transport problems.
Robustness means that the error estimates are uniform with respect to
vanishing diffusion coefficients.
The a posteriori error estimates give upper bounds for the error in the
L^1 norm between the exact solution and the approximate solution.
Hereby, the upper bounds only depend on computable constants and the
approximate solution itself. Therefore, the upper bound can be computed.
Using these theoretical results adaptive solution strategies are deduced,
implemented and tested for some model problems.
These adaptive techniques are applicable e.g. in two phase flow problems in
porous media or in the simulation of subsurface contaminant transport processes.
For two phase flow and density driven flow in porous media the applicability
is shown in several examples.","abstract_html":"In this thesis we derive robust a posteriori error estimates <br>for finite volume approximations of convection dominated nonlinear <br>transport problems. <br>Robustness means that the error estimates are uniform with respect to <br>vanishing diffusion coefficients. <br>The a posteriori error estimates give upper bounds for the error in the <br>L^1 norm between the exact solution and the approximate solution. <br>Hereby, the upper bounds only depend on computable constants and the <br>approximate solution itself. Therefore, the upper bound can be computed. <br>Using these theoretical results adaptive solution strategies are deduced, <br>implemented and tested for some model problems. <br>These adaptive techniques are applicable e.g. in two phase flow problems in <br>porous media or in the simulation of subsurface contaminant transport processes. <br>For two phase flow and density driven flow in porous media the applicability <br>is shown in several examples.","abstract_has_math":false,"creators":["Ohlberger, Mario"],"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":"2026-07-24T02:21:30Z","subjects":["A posteriori Fehlerabschätzungen, adaptive Verfahren","konvektionsdominante Probleme,","A posteriori error estimates","adaptive methods","finite volume","convection dominated","unstructured grids"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://freidok.uni-freiburg.de/data/178","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":["Ohlberger, Mario"]}]},{"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 Fehlerabschätzungen, adaptive Verfahren","konvektionsdominante Probleme,","A posteriori error estimates","adaptive methods","finite volume","convection dominated","unstructured grids"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis we derive robust a posteriori error estimates
for finite volume approximations of convection dominated nonlinear
transport problems.
Robustness means that the error estimates are uniform with respect to
vanishing diffusion coefficients.
The a posteriori error estimates give upper bounds for the error in the
L^1 norm between the exact solution and the approximate solution.
Hereby, the upper bounds only depend on computable constants and the
approximate solution itself. Therefore, the upper bound can be computed.
Using these theoretical results adaptive solution strategies are deduced,
implemented and tested for some model problems.
These adaptive techniques are applicable e.g. in two phase flow problems in
porous media or in the simulation of subsurface contaminant transport processes.
For two phase flow and density driven flow in porous media the applicability
is shown in several examples."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["A posteriori error estimates and adaptive methods for convection dominated transport processes","A posteriori Fehlerabschätzungen und adaptive Methoden für konvektionsdominante Transportprozesse"]}]}],"canonical_facts":{"dc:contributor":["Kröner, Dietmar"],"dc:creator":["Ohlberger, Mario"],"dc:description.abstract":["In this thesis we derive robust a posteriori error estimates
for finite volume approximations of convection dominated nonlinear
transport problems.
Robustness means that the error estimates are uniform with respect to
vanishing diffusion coefficients.
The a posteriori error estimates give upper bounds for the error in the
L^1 norm between the exact solution and the approximate solution.
Hereby, the upper bounds only depend on computable constants and the
approximate solution itself. Therefore, the upper bound can be computed.
Using these theoretical results adaptive solution strategies are deduced,
implemented and tested for some model problems.
These adaptive techniques are applicable e.g. in two phase flow problems in
porous media or in the simulation of subsurface contaminant transport processes.
For two phase flow and density driven flow in porous media the applicability
is shown in several examples."],"dc:format.medium":["application/pdf"],"dc:subject":["A posteriori Fehlerabschätzungen, adaptive Verfahren","konvektionsdominante Probleme,","A posteriori error estimates","adaptive methods","finite volume","convection dominated","unstructured grids"],"dc:title":["A posteriori error estimates and adaptive methods for convection dominated transport processes","A posteriori Fehlerabschätzungen und adaptive Methoden für konvektionsdominante Transportprozesse"],"dc:type":["DoctoralThesis"]},"updated_at":"2026-07-24T02:21:30Z"}