{"id":"https://openalex.org/W2036957339","doi":"https://doi.org/10.1137/s0036142903434874","title":"Fully Discrete Finite Element Approximation for Anisotropic Surface Diffusion of Graphs","display_name":"Fully Discrete Finite Element Approximation for Anisotropic Surface Diffusion of Graphs","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2036957339","doi":"https://doi.org/10.1137/s0036142903434874","mag":"2036957339"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142903434874","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142903434874","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073230253","display_name":"Klaus Deckelnick","orcid":null},"institutions":[{"id":"https://openalex.org/I95793202","display_name":"Otto-von-Guericke-Universit\u00e4t Magdeburg","ror":"https://ror.org/00ggpsq73","country_code":"DE","type":"education","lineage":["https://openalex.org/I95793202"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Klaus Deckelnick","raw_affiliation_strings":["Otto von Guericke University Magdeburg\u00a0"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Otto von Guericke University Magdeburg\u00a0","institution_ids":["https://openalex.org/I95793202"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089965962","display_name":"Gerhard Dziuk","orcid":null},"institutions":[{"id":"https://openalex.org/I161046081","display_name":"University of Freiburg","ror":"https://ror.org/0245cg223","country_code":"DE","type":"education","lineage":["https://openalex.org/I161046081"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gerhard Dziuk","raw_affiliation_strings":["Albert-Ludwigs-University of Freiburg"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Albert-Ludwigs-University of Freiburg","institution_ids":["https://openalex.org/I161046081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027234006","display_name":"Charles M. Elliott","orcid":"https://orcid.org/0000-0002-6924-4455"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Charles M. Elliott","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.8624,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.93373807,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"43","issue":"3","first_page":"1112","last_page":"1138"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12141","display_name":"Fluid Dynamics and Thin Films","score":0.9915000200271606,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9771999716758728,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.848764955997467},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.8023259043693542},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.5650238394737244},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5624609589576721},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5097941756248474},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.5076066255569458},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5003271102905273},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4791621267795563},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4785269498825073},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.47413063049316406},{"id":"https://openalex.org/keywords/anisotropic-diffusion","display_name":"Anisotropic diffusion","score":0.4470519423484802},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4423026740550995},{"id":"https://openalex.org/keywords/anisotropy","display_name":"Anisotropy","score":0.4219904839992523},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39998146891593933},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21173101663589478},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06182369589805603}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.848764955997467},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8023259043693542},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.5650238394737244},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5624609589576721},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5097941756248474},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.5076066255569458},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5003271102905273},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4791621267795563},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4785269498825073},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.47413063049316406},{"id":"https://openalex.org/C203504353","wikidata":"https://www.wikidata.org/wiki/Q4765461","display_name":"Anisotropic diffusion","level":3,"score":0.4470519423484802},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4423026740550995},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.4219904839992523},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39998146891593933},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21173101663589478},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06182369589805603},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036142903434874","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142903434874","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:freidok.uni-freiburg.de:56971","is_oa":false,"landing_page_url":"https://freidok.uni-freiburg.de/data/56971","pdf_url":null,"source":{"id":"https://openalex.org/S4306401057","display_name":"FreiDok plus (Universit\u00e4tsbibliothek Freiburg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I161046081","host_organization_name":"University of Freiburg","host_organization_lineage":["https://openalex.org/I161046081"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Numerical Analysis. - 43, 3 (2005) , 1112-1138, ISSN: 0036-1429","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W154326642","https://openalex.org/W346943483","https://openalex.org/W1965753687","https://openalex.org/W1967307040","https://openalex.org/W1979743485","https://openalex.org/W1989835079","https://openalex.org/W2002826252","https://openalex.org/W2003173073","https://openalex.org/W2008777025","https://openalex.org/W2010432344","https://openalex.org/W2017334281","https://openalex.org/W2018251972","https://openalex.org/W2023561448","https://openalex.org/W2034647847","https://openalex.org/W2049515073","https://openalex.org/W2067241014","https://openalex.org/W2076068357","https://openalex.org/W2085945334","https://openalex.org/W2102605119","https://openalex.org/W2148524643","https://openalex.org/W2160010354","https://openalex.org/W2166714473"],"related_works":["https://openalex.org/W2407139927","https://openalex.org/W2105274892","https://openalex.org/W2389517732","https://openalex.org/W2368979295","https://openalex.org/W3009892721","https://openalex.org/W4388482258","https://openalex.org/W2109336326","https://openalex.org/W2337838060","https://openalex.org/W2028921745","https://openalex.org/W2353970138"],"abstract_inverted_index":{"We":[0,59],"analyze":[1],"a":[2],"fully":[3],"discrete":[4],"numerical":[5,69],"scheme":[6,21,66],"for":[7,13,32,63],"approximating":[8],"the":[9,25,33,64],"evolution":[10],"of":[11,27],"graphs":[12],"surfaces":[14],"evolving":[15],"by":[16,50],"anisotropic":[17],"surface":[18,78],"diffusion.":[19,79],"The":[20,54],"is":[22,57],"based":[23],"on":[24],"idea":[26],"second":[28,44],"order":[29,37,45],"operator":[30],"splitting":[31],"nonlinear":[34],"geometric":[35],"fourth":[36],"equation.":[38],"This":[39],"yields":[40],"two":[41],"coupled":[42],"spatially":[43],"problems,":[46],"which":[47],"are":[48],"approximated":[49],"linear":[51],"finite":[52],"elements.":[53],"time":[55],"discretization":[56],"semi-implicit.":[58],"prove":[60],"error":[61],"bounds":[62],"resulting":[65],"and":[67,76],"present":[68],"test":[70],"calculations":[71],"that":[72],"confirm":[73],"our":[74],"analysis":[75],"illustrate":[77]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}