{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/49379"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/49379","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Investigation of stability and accuracy of high order generalized finite element methods","abstract":"The Generalized Finite Element methods (GFEMs) is a family of discretization methods which are based on the partition of unity (PoU) concept and are able to provide users with flexibility in choosing enrichments to approximate the target problem. The quality of the resulting approximation can be judged by the accuracy and its convergence rate, the conditioning and its growth rate. A major type of GFEM enrichment is the polynomial enrichment. Based on that, several modified versions of enrichments can be formulated and adopted in the simulation yielding different approximation behaviors in terms of accuracy and conditioning. By solving a one-dimensional problem and a two-dimensional problem, this report compares the numerical behaviors for different discretization methods including p-Lagrange FEM, p-hierarchical FEM, GFEM, stable GFEM (SGFEM) which is a recently proposed method with improved conditioning, and a number of variations on the GFEM and SGFEM. Other aspects considered are the linear dependency (LD) issue, the effect of mesh perturbation, and the factorization time. They are also presented to provide the reader with a broader knowledge of GFEMs.","abstract_html":"The Generalized Finite Element methods (GFEMs) is a family of discretization methods which are based on the partition of unity (PoU) concept and are able to provide users with flexibility in choosing enrichments to approximate the target problem. The quality of the resulting approximation can be judged by the accuracy and its convergence rate, the conditioning and its growth rate. A major type of GFEM enrichment is the polynomial enrichment. Based on that, several modified versions of enrichments can be formulated and adopted in the simulation yielding different approximation behaviors in terms of accuracy and conditioning. By solving a one-dimensional problem and a two-dimensional problem, this report compares the numerical behaviors for different discretization methods including p-Lagrange FEM, p-hierarchical FEM, GFEM, stable GFEM (SGFEM) which is a recently proposed method with improved conditioning, and a number of variations on the GFEM and SGFEM. Other aspects considered are the linear dependency (LD) issue, the effect of mesh perturbation, and the factorization time. They are also presented to provide the reader with a broader knowledge of GFEMs.","abstract_has_math":false,"creators":["Li, Haoyang"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Civil Engineering","degree_department":null,"school":null,"contributors":["Duarte, C. Armando"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-05-30T16:41:01Z","date_published":"2014-05-30T16:41:01Z","updated_at":"2026-07-22T22:25:38Z","subjects":["Generalized Finite Element Method (GFEM)","stable generalized finite element method","convergence analysis","conditioning analysis","high order","polynomial enrichment"],"languages":["en"],"rights":["Copyright 2014 Haoyang Li"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/49379","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Duarte, C. Armando"]},{"key":"dc:creator","label":"Author","values":["Li, Haoyang"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-05-30T16:41:01Z","2014-05"]},{"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":["Generalized Finite Element Method (GFEM)","stable generalized finite element method","convergence analysis","conditioning analysis","high order","polynomial enrichment"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2014 Haoyang Li"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/49379"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The Generalized Finite Element methods (GFEMs) is a family of discretization methods which are based on the partition of unity (PoU) concept and are able to provide users with flexibility in choosing enrichments to approximate the target problem. The quality of the resulting approximation can be judged by the accuracy and its convergence rate, the conditioning and its growth rate. A major type of GFEM enrichment is the polynomial enrichment. Based on that, several modified versions of enrichments can be formulated and adopted in the simulation yielding different approximation behaviors in terms of accuracy and conditioning. By solving a one-dimensional problem and a two-dimensional problem, this report compares the numerical behaviors for different discretization methods including p-Lagrange FEM, p-hierarchical FEM, GFEM, stable GFEM (SGFEM) which is a recently proposed method with improved conditioning, and a number of variations on the GFEM and SGFEM. Other aspects considered are the linear dependency (LD) issue, the effect of mesh perturbation, and the factorization time. They are also presented to provide the reader with a broader knowledge of GFEMs.","Item withdrawn by Laura Spradlin (lspradl2@illinois.edu) on 2014-05-01T18:10:33Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Li_Haoyang.pdf: 1844666 bytes, checksum: 0ac29431fd52a65b3508fa9267b517dc (MD5)","Made available in DSpace on 2014-05-30T16:41:01Z (GMT). No. of bitstreams: 2 Haoyang_Li.pdf: 1844666 bytes, checksum: 0ac29431fd52a65b3508fa9267b517dc (MD5) license.txt: 4057 bytes, checksum: 00bf773e40dbd1093416f659f097bfbb (MD5)"]},{"key":"dc:title","label":"Title","values":["Investigation of stability and accuracy of high order generalized finite element methods"]}]}],"canonical_facts":{"dc:contributor":["Duarte, C. Armando"],"dc:creator":["Li, Haoyang"],"dc:date":["2014-05-30T16:41:01Z","2014-05"],"dc:description":["The Generalized Finite Element methods (GFEMs) is a family of discretization methods which are based on the partition of unity (PoU) concept and are able to provide users with flexibility in choosing enrichments to approximate the target problem. The quality of the resulting approximation can be judged by the accuracy and its convergence rate, the conditioning and its growth rate. A major type of GFEM enrichment is the polynomial enrichment. Based on that, several modified versions of enrichments can be formulated and adopted in the simulation yielding different approximation behaviors in terms of accuracy and conditioning. By solving a one-dimensional problem and a two-dimensional problem, this report compares the numerical behaviors for different discretization methods including p-Lagrange FEM, p-hierarchical FEM, GFEM, stable GFEM (SGFEM) which is a recently proposed method with improved conditioning, and a number of variations on the GFEM and SGFEM. Other aspects considered are the linear dependency (LD) issue, the effect of mesh perturbation, and the factorization time. They are also presented to provide the reader with a broader knowledge of GFEMs.","Item withdrawn by Laura Spradlin (lspradl2@illinois.edu) on 2014-05-01T18:10:33Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Li_Haoyang.pdf: 1844666 bytes, checksum: 0ac29431fd52a65b3508fa9267b517dc (MD5)","Made available in DSpace on 2014-05-30T16:41:01Z (GMT). No. of bitstreams: 2 Haoyang_Li.pdf: 1844666 bytes, checksum: 0ac29431fd52a65b3508fa9267b517dc (MD5) license.txt: 4057 bytes, checksum: 00bf773e40dbd1093416f659f097bfbb (MD5)"],"dc:identifier":["http://hdl.handle.net/2142/49379"],"dc:language":["en"],"dc:rights":["Copyright 2014 Haoyang Li"],"dc:subject":["Generalized Finite Element Method (GFEM)","stable generalized finite element method","convergence analysis","conditioning analysis","high order","polynomial enrichment"],"dc:title":["Investigation of stability and accuracy of high order generalized finite element methods"],"dc:type":["text"],"thesis:degree_discipline":["Civil Engineering"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:38Z"}