{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/66442"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/66442","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Self Adaptive Methods for Parabolic Partial Differential Equations","abstract":"In many applications, the solutions to important partial differential equations are characterized by a sharp active region of transition (such as wave fronts or areas of rapid diffusion) surrounded by relatively calm stable regions. The numerical approximation to such a solution is based on a mesh or grid structure that is best when very fine in the active region and coarse in the calm region.","abstract_html":"In many applications, the solutions to important partial differential equations are characterized by a sharp active region of transition (such as wave fronts or areas of rapid diffusion) surrounded by relatively calm stable regions. The numerical approximation to such a solution is based on a mesh or grid structure that is best when very fine in the active region and coarse in the calm region.","abstract_has_math":false,"creators":["Gannon, Dennis Brooke"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-13T18:02:16Z","date_published":"2014-12-13T18:02:16Z","updated_at":"2026-07-22T22:25:55Z","subjects":["Computer Science"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8108510"],"render_values":[{"text":"(UMI)AAI8108510","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/66442","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Gannon, Dennis Brooke"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-13T18:02:16Z","10000-01-01","1980"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"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":["Computer Science"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/66442","(UMI)AAI8108510"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In many applications, the solutions to important partial differential equations are characterized by a sharp active region of transition (such as wave fronts or areas of rapid diffusion) surrounded by relatively calm stable regions. The numerical approximation to such a solution is based on a mesh or grid structure that is best when very fine in the active region and coarse in the calm region.","This work considers algorithms for the proper construction of locally refined grids for finite element based methods for the solution to such problems. By extending the work of Babuska and Rheinboldt to the case of parabolic problems, refinement criteria are developed and tested for this class of problems.","The computational complexity of such a strategy is studied, and algorithms based on nested dissection are presented to solve the associated linear algebra problems.","Made available in DSpace on 2014-12-13T18:02:16Z (GMT). No. of bitstreams: 1 8108510.pdf: 2432065 bytes, checksum: 397a5ac85a661c6e9e595ae895ed2d37 (MD5) Previous issue date: 1980","Embargo set by: Seth Robbins for item 66620 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","92 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1980."]},{"key":"dc:title","label":"Title","values":["Self Adaptive Methods for Parabolic Partial Differential Equations"]}]}],"canonical_facts":{"dc:creator":["Gannon, Dennis Brooke"],"dc:date":["2014-12-13T18:02:16Z","10000-01-01","1980"],"dc:description":["In many applications, the solutions to important partial differential equations are characterized by a sharp active region of transition (such as wave fronts or areas of rapid diffusion) surrounded by relatively calm stable regions. The numerical approximation to such a solution is based on a mesh or grid structure that is best when very fine in the active region and coarse in the calm region.","This work considers algorithms for the proper construction of locally refined grids for finite element based methods for the solution to such problems. By extending the work of Babuska and Rheinboldt to the case of parabolic problems, refinement criteria are developed and tested for this class of problems.","The computational complexity of such a strategy is studied, and algorithms based on nested dissection are presented to solve the associated linear algebra problems.","Made available in DSpace on 2014-12-13T18:02:16Z (GMT). No. of bitstreams: 1 8108510.pdf: 2432065 bytes, checksum: 397a5ac85a661c6e9e595ae895ed2d37 (MD5) Previous issue date: 1980","Embargo set by: Seth Robbins for item 66620 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","92 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1980."],"dc:identifier":["http://hdl.handle.net/2142/66442","(UMI)AAI8108510"],"dc:language":["eng"],"dc:subject":["Computer Science"],"dc:title":["Self Adaptive Methods for Parabolic Partial Differential Equations"],"dc:type":["text"],"thesis:degree_discipline":["Computer Science"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:55Z"}