{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/23090"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/23090","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"A Two-Level Method For The Steady-State Quasigeostrophic Equation","abstract":"The quasi-geostrophic equations (QGE) are a model of large-scale ocean flows. We consider a pure stream function formulation and cite results for optimal error estimates for finding approximate solutions with the finite element method. We examine both the time dependent and steady-state versions of the equations. Numerical experiments verify the error estimates. We examine the Argyris finite element and derive the transformation matrix necessary to perform calculations on the reference triangle. We use the Argyris element because it is a high-order, conforming finite element for fourth order problems. In order to increase computational efficiency, we consider a two-level method to linearize the system of equations. This allows us to solve a small, nonlinear system and then use the result to linearize a larger system.","abstract_html":"The quasi-geostrophic equations (QGE) are a model of large-scale ocean flows. We consider a pure stream function formulation and cite results for optimal error estimates for finding approximate solutions with the finite element method. We examine both the time dependent and steady-state versions of the equations. Numerical experiments verify the error estimates. We examine the Argyris finite element and derive the transformation matrix necessary to perform calculations on the reference triangle. We use the Argyris element because it is a high-order, conforming finite element for fourth order problems. In order to increase computational efficiency, we consider a two-level method to linearize the system of equations. This allows us to solve a small, nonlinear system and then use the result to linearize a larger system.","abstract_has_math":false,"creators":["Wells, David Reese"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Mathematics","degree_department":"Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Iliescu, Traian"],"committee_members":["Lin, Tao","Adjerid, Slimane"],"year":2013,"date_issued":"2013-05-23","date_published":"2013-05-23","updated_at":"2026-07-22T22:20:03Z","subjects":["Quasi-geostrophic equations","Finite element method","Argyris Element","Two-Level Method"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:861"],"render_values":[{"text":"vt_gsexam:861","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/23090","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Iliescu, Traian"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Lin, Tao","Adjerid, Slimane"]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Wells, David Reese"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2013-05-24T08:01:13Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2013-05-24T08:01:13Z"]},{"key":"dc:date.issued","label":"Date","values":["2013-05-23"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Quasi-geostrophic equations","Finite element method","Argyris Element","Two-Level Method"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:861"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/23090"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The quasi-geostrophic equations (QGE) are a model of large-scale ocean flows. We consider a pure stream function formulation and cite results for optimal error estimates for finding approximate solutions with the finite element method. We examine both the time dependent and steady-state versions of the equations. Numerical experiments verify the error estimates. We examine the Argyris finite element and derive the transformation matrix necessary to perform calculations on the reference triangle. We use the Argyris element because it is a high-order, conforming finite element for fourth order problems. In order to increase computational efficiency, we consider a two-level method to linearize the system of equations. 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We examine both the time dependent and steady-state versions of the equations. Numerical experiments verify the error estimates. We examine the Argyris finite element and derive the transformation matrix necessary to perform calculations on the reference triangle. We use the Argyris element because it is a high-order, conforming finite element for fourth order problems. In order to increase computational efficiency, we consider a two-level method to linearize the system of equations. 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