{"id":"https://openalex.org/W1910855269","doi":"https://doi.org/10.1137/140974407","title":"Solution of Nonlinear Stokes Equations Discretized By High-Order Finite Elements on Nonconforming and Anisotropic Meshes, with Application to Ice Sheet Dynamics","display_name":"Solution of Nonlinear Stokes Equations Discretized By High-Order Finite Elements on Nonconforming and Anisotropic Meshes, with Application to Ice Sheet Dynamics","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1910855269","doi":"https://doi.org/10.1137/140974407","mag":"1910855269"},"language":"en","primary_location":{"id":"doi:10.1137/140974407","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140974407","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1406.6573","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006603988","display_name":"Tobin Isaac","orcid":"https://orcid.org/0000-0002-2628-3585"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Tobin Isaac","raw_affiliation_strings":["University of Texas at Austin#TAB#"],"affiliations":[{"raw_affiliation_string":"University of Texas at Austin#TAB#","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012373865","display_name":"Georg Stadler","orcid":"https://orcid.org/0000-0001-7762-6544"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Georg Stadler","raw_affiliation_strings":["University of Texas at Austin","New York University"],"affiliations":[{"raw_affiliation_string":"University of Texas at Austin","institution_ids":["https://openalex.org/I86519309"]},{"raw_affiliation_string":"New York University","institution_ids":["https://openalex.org/I57206974"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049331711","display_name":"Omar Ghattas","orcid":"https://orcid.org/0000-0001-7742-2509"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Omar Ghattas","raw_affiliation_strings":["University of Texas at Austin#TAB#"],"affiliations":[{"raw_affiliation_string":"University of Texas at Austin#TAB#","institution_ids":["https://openalex.org/I86519309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5006603988"],"corresponding_institution_ids":["https://openalex.org/I86519309"],"apc_list":null,"apc_paid":null,"fwci":7.6905,"has_fulltext":false,"cited_by_count":54,"citation_normalized_percentile":{"value":0.97803698,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"37","issue":"6","first_page":"B804","last_page":"B833"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9986000061035156,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9986000061035156,"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/T11405","display_name":"Geophysics and Gravity Measurements","score":0.9923999905586243,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.986299991607666,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.9081040620803833},{"id":"https://openalex.org/keywords/schur-complement","display_name":"Schur complement","score":0.6418858766555786},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6258435249328613},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5981966853141785},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5929833650588989},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.5555833578109741},{"id":"https://openalex.org/keywords/hexahedron","display_name":"Hexahedron","score":0.5091652274131775},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5052538514137268},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.44430646300315857},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4261203408241272},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.33987855911254883},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3258745074272156},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2665882706642151},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.23605570197105408},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.16930603981018066},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11954274773597717}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.9081040620803833},{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.6418858766555786},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6258435249328613},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5981966853141785},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5929833650588989},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.5555833578109741},{"id":"https://openalex.org/C22411076","wikidata":"https://www.wikidata.org/wiki/Q668113","display_name":"Hexahedron","level":3,"score":0.5091652274131775},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5052538514137268},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.44430646300315857},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4261203408241272},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.33987855911254883},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3258745074272156},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2665882706642151},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.23605570197105408},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.16930603981018066},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11954274773597717},{"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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/140974407","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140974407","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1406.6573","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1406.6573","pdf_url":"https://arxiv.org/pdf/1406.6573","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1406.6573","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1406.6573","pdf_url":"https://arxiv.org/pdf/1406.6573","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":60,"referenced_works":["https://openalex.org/W207622524","https://openalex.org/W1480588625","https://openalex.org/W1506342804","https://openalex.org/W1520565385","https://openalex.org/W1523963696","https://openalex.org/W1575501007","https://openalex.org/W1578281258","https://openalex.org/W1965116625","https://openalex.org/W1979313559","https://openalex.org/W1988680749","https://openalex.org/W1989177281","https://openalex.org/W1996216696","https://openalex.org/W2003433978","https://openalex.org/W2003815420","https://openalex.org/W2005215526","https://openalex.org/W2007897716","https://openalex.org/W2013336356","https://openalex.org/W2020029307","https://openalex.org/W2022639074","https://openalex.org/W2024977211","https://openalex.org/W2026700187","https://openalex.org/W2032888785","https://openalex.org/W2036614641","https://openalex.org/W2041876368","https://openalex.org/W2044582720","https://openalex.org/W2048369486","https://openalex.org/W2049415037","https://openalex.org/W2055464357","https://openalex.org/W2058175297","https://openalex.org/W2072132691","https://openalex.org/W2073341634","https://openalex.org/W2075192458","https://openalex.org/W2084900853","https://openalex.org/W2088917948","https://openalex.org/W2089518656","https://openalex.org/W2089774562","https://openalex.org/W2093753671","https://openalex.org/W2101259661","https://openalex.org/W2102512732","https://openalex.org/W2104951519","https://openalex.org/W2118067965","https://openalex.org/W2119817529","https://openalex.org/W2120027408","https://openalex.org/W2125313919","https://openalex.org/W2129412583","https://openalex.org/W2130272322","https://openalex.org/W2133248904","https://openalex.org/W2139426433","https://openalex.org/W2139611370","https://openalex.org/W2142304406","https://openalex.org/W2243781021","https://openalex.org/W2332163904","https://openalex.org/W2477249138","https://openalex.org/W2969262004","https://openalex.org/W3099334783","https://openalex.org/W4234337445","https://openalex.org/W4234447426","https://openalex.org/W4246112776","https://openalex.org/W4251327120","https://openalex.org/W4293775970"],"related_works":["https://openalex.org/W2648827758","https://openalex.org/W3131769846","https://openalex.org/W2048163432","https://openalex.org/W4389317411","https://openalex.org/W1492522302","https://openalex.org/W2782457188","https://openalex.org/W2396508626","https://openalex.org/W2114969937","https://openalex.org/W4236665358","https://openalex.org/W2138197125"],"abstract_inverted_index":{"Motivated":[0],"by":[1],"the":[2,10,13,27,56,72,87,101,118,121,125,155,177,217,221,236,243,251,261],"need":[3],"for":[4,26,86,161,176,188,193,267],"efficient":[5,146],"and":[6,23,46,55,103,124,166,182,226,230,259],"accurate":[7],"simulation":[8],"of":[9,12,29,94,100,104,120,127,216,223,227,250,264],"dynamics":[11,45],"polar":[14],"ice":[15,44,162,244,253],"sheets,":[16],"we":[17,75,205],"design":[18],"high-order":[19,122],"finite":[20,60,114,238],"element":[21,61,218,239],"discretizations":[22],"scalable":[24],"solvers":[25],"solution":[28],"nonlinear":[30,73],"incompressible":[31],"Stokes":[32,89],"equations.":[33],"We":[34,50,164,241],"focus":[35],"on":[36,117,147,235],"power-law,":[37],"shear":[38],"thinning":[39],"rheologies":[40],"used":[41],"in":[42,196,246],"modeling":[43],"other":[47],"geophysical":[48],"flows.":[49],"use":[51],"nonconforming":[52,224],"hexahedral":[53],"meshes":[54],"conforming":[57],"inf-sup":[58],"stable":[59],"velocity-pressure":[62],"pairings":[63],"$\\mathbb{Q}_k\\times":[64],"\\mathbb{Q}^\\text{disc}_{k-2}$":[65],"or":[66],"$\\mathbb{Q}_k":[67],"\\times":[68],"\\mathbb{P}^\\text{disc}_{k-1}$.":[69],"To":[70],"solve":[71],"equations,":[74],"propose":[76],"a":[77,81,183,202,247],"Newton-Krylov":[78],"method":[79],"with":[80,135,269],"block":[82],"upper":[83],"triangular":[84],"preconditioner":[85,96,141],"linearized":[88],"systems.":[90],"The":[91,108],"diagonal":[92],"blocks":[93],"this":[95],"are":[97,151],"sparse":[98],"approximations":[99],"(1,1)-block":[102,109],"its":[105,128],"Schur":[106],"complement.":[107],"is":[110,130,142,214],"approximated":[111,131],"using":[112,132],"linear":[113],"elements":[115],"based":[116],"nodes":[119],"discretization,":[123],"application":[126],"inverse":[129],"algebraic":[133],"multigrid":[134],"an":[136],"incomplete":[137],"factorization":[138],"smoother.":[139],"This":[140],"designed":[143],"to":[144,153,170,271],"be":[145],"anisotropic":[148],"meshes,":[149],"which":[150],"necessary":[152],"match":[154],"high":[156,197],"aspect":[157,198,219],"ratio":[158,199],"domains":[159],"typical":[160],"sheets.":[163],"develop":[165],"make":[167],"available":[168],"extensions":[169],"two":[171],"libraries---a":[172],"hybrid":[173],"meshing":[174],"scheme":[175,187],"p4est":[178],"parallel":[179,262],"AMR":[180],"library,":[181],"modified":[184],"smoothed":[185],"aggregation":[186],"PETSc---to":[189],"improve":[190],"their":[191],"support":[192],"solving":[194],"PDEs":[195],"domains.":[200],"In":[201],"numerical":[203],"study,":[204],"find":[206],"that":[207,213,231],"our":[208,265],"solver":[209,266],"yields":[210],"fast":[211],"convergence":[212],"independent":[215],"ratio,":[220],"occurrence":[222],"interfaces,":[225],"mesh":[228],"refinement,":[229],"depends":[232],"only":[233],"weakly":[234],"polynomial":[237],"order.":[240],"simulate":[242],"flow":[245],"realistic":[248],"description":[249],"Antarctic":[252],"sheet":[254],"derived":[255],"from":[256],"field":[257],"data,":[258],"study":[260],"scalability":[263],"problems":[268],"up":[270],"383M":[272],"unknowns.":[273]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2016-06-24T00:00:00"}