{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/105935"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/105935","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"A stabilized discontinuous Galerkin method for variational embedding of physics-based data","abstract":"A stabilized variational framework that admits overlapping as well as non overlapping coupling of domains for a variety of Partial Differential Equations (PDEs) is employed in this work. This method accommodates non-matching meshes across the interfaces between the subdomain boundaries and allows for sharp changes in mechanical material properties. Interface coupling operators that emanate via embedding of Discontinuous Galerkin ideas in the continuous Galerkin framework provide a unique avenue to embed physics-based data in the modeling and analysis of the system. Physics-based data, either in discrete or in distributed form can be embedded via the interface operators that are otherwise devised to enforce continuity of the fields across internal discontinuities. The least-squares form of the interface coupling operators is exploited for its inherent linear regression type structure, and it is shown that it helps improve the overall accuracy of the numerical solution. Method is applicable to multi-PDE class of problems wherein different PDEs are operational on adjacent domains across the common interface. The method also comes equipped with a residual based error estimation method which is shown to be applicable to test problems employed. Different test cases are employed to investigate the mathematical attributes of the method.","abstract_html":"A stabilized variational framework that admits overlapping as well as non overlapping coupling of domains for a variety of Partial Differential Equations (PDEs) is employed in this work. This method accommodates non-matching meshes across the interfaces between the subdomain boundaries and allows for sharp changes in mechanical material properties. Interface coupling operators that emanate via embedding of Discontinuous Galerkin ideas in the continuous Galerkin framework provide a unique avenue to embed physics-based data in the modeling and analysis of the system. Physics-based data, either in discrete or in distributed form can be embedded via the interface operators that are otherwise devised to enforce continuity of the fields across internal discontinuities. The least-squares form of the interface coupling operators is exploited for its inherent linear regression type structure, and it is shown that it helps improve the overall accuracy of the numerical solution. Method is applicable to multi-PDE class of problems wherein different PDEs are operational on adjacent domains across the common interface. The method also comes equipped with a residual based error estimation method which is shown to be applicable to test problems employed. Different test cases are employed to investigate the mathematical attributes of the method.","abstract_has_math":false,"creators":["Goraya, Shoaib Ahmad"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Civil Engineering","degree_department":null,"school":null,"contributors":["Masud, Arif"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-11-26T20:59:45Z","date_published":"2019-11-26T20:59:45Z","updated_at":"2026-07-22T22:24:45Z","subjects":["Variational Multiscale","Discontinuous Galerkin","Interfaces","Data","Multiple PDEs","Multiscale Methods","Linear Elasticity","Stokes Flow","Darcy Flow","Stokes-Darcy Flow","Mixed Elasticity","Stabilized Methods","Residual-free Bubbles","Posteriori Error Estimation"],"languages":["en"],"rights":["Copyright 2019 Shoaib Ahmad Goraya"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/105935","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Masud, Arif"]},{"key":"dc:creator","label":"Author","values":["Goraya, Shoaib Ahmad"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019-11-26T20:59:45Z","2021-11-27T10:15:34Z","2019-07-15","2019-08"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Civil Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Variational Multiscale","Discontinuous Galerkin","Interfaces","Data","Multiple PDEs","Multiscale Methods","Linear Elasticity","Stokes Flow","Darcy Flow","Stokes-Darcy Flow","Mixed Elasticity","Stabilized Methods","Residual-free Bubbles","Posteriori Error Estimation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2019 Shoaib Ahmad Goraya"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/105935"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A stabilized variational framework that admits overlapping as well as non overlapping coupling of domains for a variety of Partial Differential Equations (PDEs) is employed in this work. This method accommodates non-matching meshes across the interfaces between the subdomain boundaries and allows for sharp changes in mechanical material properties. Interface coupling operators that emanate via embedding of Discontinuous Galerkin ideas in the continuous Galerkin framework provide a unique avenue to embed physics-based data in the modeling and analysis of the system. Physics-based data, either in discrete or in distributed form can be embedded via the interface operators that are otherwise devised to enforce continuity of the fields across internal discontinuities. The least-squares form of the interface coupling operators is exploited for its inherent linear regression type structure, and it is shown that it helps improve the overall accuracy of the numerical solution. Method is applicable to multi-PDE class of problems wherein different PDEs are operational on adjacent domains across the common interface. The method also comes equipped with a residual based error estimation method which is shown to be applicable to test problems employed. Different test cases are employed to investigate the mathematical attributes of the method.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2021-08-01","The student, Shoaib Ahmad Goraya, accepted the attached license on 2019-07-12 at 16:53.","The student, Shoaib Ahmad Goraya, submitted this Thesis for approval on 2019-07-12 at 16:54.","This Thesis was approved for publication on 2019-07-15 at 14:47.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14260 on 2019-11-26 at 14:03:50","Made available in DSpace on 2019-11-26T20:59:45Z (GMT). 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This method accommodates non-matching meshes across the interfaces between the subdomain boundaries and allows for sharp changes in mechanical material properties. Interface coupling operators that emanate via embedding of Discontinuous Galerkin ideas in the continuous Galerkin framework provide a unique avenue to embed physics-based data in the modeling and analysis of the system. Physics-based data, either in discrete or in distributed form can be embedded via the interface operators that are otherwise devised to enforce continuity of the fields across internal discontinuities. The least-squares form of the interface coupling operators is exploited for its inherent linear regression type structure, and it is shown that it helps improve the overall accuracy of the numerical solution. Method is applicable to multi-PDE class of problems wherein different PDEs are operational on adjacent domains across the common interface. The method also comes equipped with a residual based error estimation method which is shown to be applicable to test problems employed. Different test cases are employed to investigate the mathematical attributes of the method.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2021-08-01","The student, Shoaib Ahmad Goraya, accepted the attached license on 2019-07-12 at 16:53.","The student, Shoaib Ahmad Goraya, submitted this Thesis for approval on 2019-07-12 at 16:54.","This Thesis was approved for publication on 2019-07-15 at 14:47.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14260 on 2019-11-26 at 14:03:50","Made available in DSpace on 2019-11-26T20:59:45Z (GMT). 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