{"id":{"repo_id":"houston","oai_identifier":"oai:uh-ir.tdl.org:10657/3434"},"canonical_url":"https://search.dev.ndltd.org/etd/houston/oai:uh-ir.tdl.org:10657/3434","repository":{"repo_id":"houston","name":"University of Houston","base_url":"https://uh-ir.tdl.org/server/oai/request"},"display":{"title":"Numerical Simulation of 4th Order Total Variation Flow Problem by using C^0 IPDG Method","abstract":"This dissertation is devoted to the the numerical solution of the regularized fourth order total variation flow problem in material science representing surface relaxation below the roughening temperature. Based on regularization and a scaling in time and space, the problem is discretized implicitly in time by the backward Euler scheme and discretized in space by C$^0$ Interior Penalty Discontinuous Galerkin (C$^0$IPDG) method. In particular, it is showed that at each time instant the C$^0$IPDG approximation represents the necessary and sufficient optimality condition for the minimization of an associated proper convex, coercive, and lower semi-continuous objective functional. The main results are a priori error estimates of the global discretization error in a mesh dependent C$^0$IPDG-norm and the L$^2$-norm. A documentation of numerical results is provided illustrating the performance of the C$^0$IPDG method and predictor corrector continuation strategies.","abstract_html":"This dissertation is devoted to the the numerical solution of the regularized fourth order total variation flow problem in material science representing surface relaxation below the roughening temperature. Based on regularization and a scaling in time and space, the problem is discretized implicitly in time by the backward Euler scheme and discretized in space by C<span class=\"etd-inline-math\"><sup>0</sup></span> Interior Penalty Discontinuous Galerkin (C<span class=\"etd-inline-math\"><sup>0</sup></span>IPDG) method. In particular, it is showed that at each time instant the C<span class=\"etd-inline-math\"><sup>0</sup></span>IPDG approximation represents the necessary and sufficient optimality condition for the minimization of an associated proper convex, coercive, and lower semi-continuous objective functional. The main results are a priori error estimates of the global discretization error in a mesh dependent C<span class=\"etd-inline-math\"><sup>0</sup></span>IPDG-norm and the L<span class=\"etd-inline-math\"><sup>2</sup></span>-norm. A documentation of numerical results is provided illustrating the performance of the C<span class=\"etd-inline-math\"><sup>0</sup></span>IPDG method and predictor corrector continuation strategies.","abstract_has_math":true,"creators":["Bhandari, Chandi Prasad 1985-"],"institution":"University of Houston","degree_name":"Doctor of Philosophy","degree_level":"Doctoral","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":["Hoppe, Ronald W."],"committee_chairs":[],"committee_members":["Pan, Tsorng-Whay","Sanders, Richard","Sharma, Natasha S."],"year":2018,"date_issued":"2018-05","date_published":"2018-05","updated_at":"2026-07-24T02:31:42Z","subjects":["Surface relaxation","Galerkin approximation","C 0 Interior Penalty","Discontinuous Galerkin Approximation","Mixed finite element methods"],"languages":["eng"],"rights":["The author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s)."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10657/3434","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Hoppe, Ronald W."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Pan, Tsorng-Whay","Sanders, Richard","Sharma, Natasha S."]},{"key":"dc:creator","label":"Author","values":["Bhandari, Chandi Prasad 1985-"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2018-11-30T15:43:49Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2018-11-30T15:43:49Z"]},{"key":"dc:date.issued","label":"Date","values":["2018-05"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Houston"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Surface relaxation","Galerkin approximation","C 0 Interior Penalty","Discontinuous Galerkin Approximation","Mixed finite element methods"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["The author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s)."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10657/3434"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This dissertation is devoted to the the numerical solution of the regularized fourth order total variation flow problem in material science representing surface relaxation below the roughening temperature. Based on regularization and a scaling in time and space, the problem is discretized implicitly in time by the backward Euler scheme and discretized in space by C$^0$ Interior Penalty Discontinuous Galerkin (C$^0$IPDG) method. In particular, it is showed that at each time instant the C$^0$IPDG approximation represents the necessary and sufficient optimality condition for the minimization of an associated proper convex, coercive, and lower semi-continuous objective functional. The main results are a priori error estimates of the global discretization error in a mesh dependent C$^0$IPDG-norm and the L$^2$-norm. A documentation of numerical results is provided illustrating the performance of the C$^0$IPDG method and predictor corrector continuation strategies."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Numerical Simulation of 4th Order Total Variation Flow Problem by using C^0 IPDG Method"]}]}],"canonical_facts":{"dc:contributor.advisor":["Hoppe, Ronald W."],"dc:contributor.committeemember":["Pan, Tsorng-Whay","Sanders, Richard","Sharma, Natasha S."],"dc:creator":["Bhandari, Chandi Prasad 1985-"],"dc:date.accessioned":["2018-11-30T15:43:49Z"],"dc:date.available":["2018-11-30T15:43:49Z"],"dc:date.issued":["2018-05"],"dc:description.abstract":["This dissertation is devoted to the the numerical solution of the regularized fourth order total variation flow problem in material science representing surface relaxation below the roughening temperature. Based on regularization and a scaling in time and space, the problem is discretized implicitly in time by the backward Euler scheme and discretized in space by C$^0$ Interior Penalty Discontinuous Galerkin (C$^0$IPDG) method. In particular, it is showed that at each time instant the C$^0$IPDG approximation represents the necessary and sufficient optimality condition for the minimization of an associated proper convex, coercive, and lower semi-continuous objective functional. The main results are a priori error estimates of the global discretization error in a mesh dependent C$^0$IPDG-norm and the L$^2$-norm. A documentation of numerical results is provided illustrating the performance of the C$^0$IPDG method and predictor corrector continuation strategies."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/10657/3434"],"dc:language.iso":["eng"],"dc:rights":["The author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s)."],"dc:subject":["Surface relaxation","Galerkin approximation","C 0 Interior Penalty","Discontinuous Galerkin Approximation","Mixed finite element methods"],"dc:title":["Numerical Simulation of 4th Order Total Variation Flow Problem by using C^0 IPDG Method"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["University of Houston"]},"updated_at":"2026-07-24T02:31:42Z"}