Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W1980377066', 'doi': 'https://doi.org/10.1090/s0025-5718-07-02080-7', 'title': 'Equilibrated residual error estimator for edge elements', 'display_name': 'Equilibrated residual error estimator for edge elements', 'publication_year': 2007, 'publication_date': '2007-11-20', 'ids': {'openalex': 'https://openalex.org/W1980377066', 'doi': 'https://doi.org/10.1090/s0025-5718-07-02080-7', 'mag': '1980377066'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.1090/s0025-5718-07-02080-7', 'pdf_url': 'https://www.ams.org/mcom/2008-77-262/S0025-5718-07-02080-7/S0025-5718-07-02080-7.pdf', 'source': {'id': 'https://openalex.org/S102439543', 'display_name': 'Mathematics of Computation', 'issn_l': '0025-5718', 'issn': ['0025-5718', '1088-6842'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310315719', 'host_organization_name': 'American Mathematical Society', 'host_organization_lineage': ['https://openalex.org/P4310315719'], 'host_organization_lineage_names': ['American Mathematical Society'], 'type': 'journal'}, 'license': 'public-domain', 'license_id': 'https://openalex.org/licenses/public-domain', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': True, 'oa_status': 'hybrid', 'oa_url': 'https://www.ams.org/mcom/2008-77-262/S0025-5718-07-02080-7/S0025-5718-07-02080-7.pdf', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5019658783', 'display_name': 'Dietrich Braess', 'orcid': 'https://orcid.org/0009-0007-7232-0299'}, 'institutions': [{'id': 'https://openalex.org/I904495901', 'display_name': 'Ruhr University Bochum', 'ror': 'https://ror.org/04tsk2644', 'country_code': 'DE', 'type': 'education', 'lineage': ['https://openalex.org/I904495901']}], 'countries': ['DE'], 'is_corresponding': False, 'raw_author_name': 'Dietrich Braess', 'raw_affiliation_strings': ['Faculty of Mathematics, Ruhr-University, D-44780 Bochum, Germany#TAB#'], 'affiliations': [{'raw_affiliation_string': 'Faculty of Mathematics, Ruhr-University, D-44780 Bochum, Germany#TAB#', 'institution_ids': ['https://openalex.org/I904495901']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5021823634', 'display_name': 'Joachim Schöberl', 'orcid': 'https://orcid.org/0000-0002-1250-5087'}, 'institutions': [{'id': 'https://openalex.org/I887968799', 'display_name': 'RWTH Aachen University', 'ror': 'https://ror.org/04xfq0f34', 'country_code': 'DE', 'type': 'education', 'lineage': ['https://openalex.org/I887968799']}], 'countries': ['DE'], 'is_corresponding': False, 'raw_author_name': 'Joachim Schöberl', 'raw_affiliation_strings': ['Center for Computational Engineering Science, RWTH Aachen University, D 52062 Aachen, Germany'], 'affiliations': [{'raw_affiliation_string': 'Center for Computational Engineering Science, RWTH Aachen University, D 52062 Aachen, Germany', 'institution_ids': ['https://openalex.org/I887968799']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 2, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 6.552, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 219, 'citation_normalized_percentile': {'value': 0.964427, 'is_in_top_1_percent': False, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 98, 'max': 99}, 'biblio': {'volume': '77', 'issue': '262', 'first_page': '651', 'last_page': '673'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10339', 'display_name': 'Advanced Numerical Methods in Computational Mathematics', 'score': 0.9999, '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': 0.9999, '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/T10514', 'display_name': 'Numerical methods in engineering', 'score': 0.9985, 'subfield': {'id': 'https://openalex.org/subfields/2211', 'display_name': 'Mechanics of Materials'}, '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/T11206', 'display_name': 'Model Reduction and Neural Networks', 'score': 0.996, 'subfield': {'id': 'https://openalex.org/subfields/3109', 'display_name': 'Statistical and Nonlinear Physics'}, 'field': {'id': 'https://openalex.org/fields/31', 'display_name': 'Physics and Astronomy'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/curl', 'display_name': 'Curl (programming language)', 'score': 0.7843184}], 'concepts': [{'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.8578866}, {'id': 'https://openalex.org/C147663694', 'wikidata': 'https://www.wikidata.org/wiki/Q1144631', 'display_name': 'Curl (programming language)', 'level': 2, 'score': 0.7843184}, {'id': 'https://openalex.org/C185429906', 'wikidata': 'https://www.wikidata.org/wiki/Q1130160', 'display_name': 'Estimator', 'level': 2, 'score': 0.7122134}, {'id': 'https://openalex.org/C155512373', 'wikidata': 'https://www.wikidata.org/wiki/Q287450', 'display_name': 'Residual', 'level': 2, 'score': 0.68770945}, {'id': 'https://openalex.org/C45374587', 'wikidata': 'https://www.wikidata.org/wiki/Q12525525', 'display_name': 'Computation', 'level': 2, 'score': 0.63607895}, {'id': 'https://openalex.org/C57691317', 'wikidata': 'https://www.wikidata.org/wiki/Q1289248', 'display_name': 'Scalar (mathematics)', 'level': 2, 'score': 0.62310255}, {'id': 'https://openalex.org/C75553542', 'wikidata': 'https://www.wikidata.org/wiki/Q178161', 'display_name': 'A priori and a posteriori', 'level': 2, 'score': 0.61285174}, {'id': 'https://openalex.org/C135628077', 'wikidata': 'https://www.wikidata.org/wiki/Q220184', 'display_name': 'Finite element method', 'level': 2, 'score': 0.609787}, {'id': 'https://openalex.org/C28826006', 'wikidata': 'https://www.wikidata.org/wiki/Q33521', 'display_name': 'Applied mathematics', 'level': 1, 'score': 0.5830411}, {'id': 'https://openalex.org/C162307627', 'wikidata': 'https://www.wikidata.org/wiki/Q204833', 'display_name': 'Enhanced Data Rates for GSM Evolution', 'level': 2, 'score': 0.5087982}, {'id': 'https://openalex.org/C14036430', 'wikidata': 'https://www.wikidata.org/wiki/Q3736076', 'display_name': 'Function (biology)', 'level': 2, 'score': 0.4437473}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.38839078}, {'id': 'https://openalex.org/C126255220', 'wikidata': 'https://www.wikidata.org/wiki/Q141495', 'display_name': 'Mathematical optimization', 'level': 1, 'score': 0.32876953}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.20050141}, {'id': 'https://openalex.org/C11413529', 'wikidata': 'https://www.wikidata.org/wiki/Q8366', 'display_name': 'Algorithm', 'level': 1, 'score': 0.17847353}, {'id': 'https://openalex.org/C105795698', 'wikidata': 'https://www.wikidata.org/wiki/Q12483', 'display_name': 'Statistics', 'level': 1, 'score': 0.13214397}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.06894025}, {'id': 'https://openalex.org/C97355855', 'wikidata': 'https://www.wikidata.org/wiki/Q11473', 'display_name': 'Thermodynamics', 'level': 1, 'score': 0.059675813}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C76155785', 'wikidata': 'https://www.wikidata.org/wiki/Q418', 'display_name': 'Telecommunications', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C138885662', 'wikidata': 'https://www.wikidata.org/wiki/Q5891', 'display_name': 'Philosophy', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C111472728', 'wikidata': 'https://www.wikidata.org/wiki/Q9471', 'display_name': 'Epistemology', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C78458016', 'wikidata': 'https://www.wikidata.org/wiki/Q840400', 'display_name': 'Evolutionary biology', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C86803240', 'wikidata': 'https://www.wikidata.org/wiki/Q420', 'display_name': 'Biology', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C199360897', 'wikidata': 'https://www.wikidata.org/wiki/Q9143', 'display_name': 'Programming language', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 2, 'locations': [{'is_oa': True, 'landing_page_url': 'https://doi.org/10.1090/s0025-5718-07-02080-7', 'pdf_url': 'https://www.ams.org/mcom/2008-77-262/S0025-5718-07-02080-7/S0025-5718-07-02080-7.pdf', 'source': {'id': 'https://openalex.org/S102439543', 'display_name': 'Mathematics of Computation', 'issn_l': '0025-5718', 'issn': ['0025-5718', '1088-6842'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310315719', 'host_organization_name': 'American Mathematical Society', 'host_organization_lineage': ['https://openalex.org/P4310315719'], 'host_organization_lineage_names': ['American Mathematical Society'], 'type': 'journal'}, 'license': 'public-domain', 'license_id': 'https://openalex.org/licenses/public-domain', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, {'is_oa': True, 'landing_page_url': 'http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.7962', 'pdf_url': 'http://www.ams.org/mcom/2008-77-262/S0025-5718-07-02080-7/S0025-5718-07-02080-7.pdf', 'source': {'id': 'https://openalex.org/S4306400349', 'display_name': 'CiteSeer X (The Pennsylvania State University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I130769515', 'host_organization_name': 'Pennsylvania State University', 'host_organization_lineage': ['https://openalex.org/I130769515'], 'host_organization_lineage_names': ['Pennsylvania State University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.1090/s0025-5718-07-02080-7', 'pdf_url': 'https://www.ams.org/mcom/2008-77-262/S0025-5718-07-02080-7/S0025-5718-07-02080-7.pdf', 'source': {'id': 'https://openalex.org/S102439543', 'display_name': 'Mathematics of Computation', 'issn_l': '0025-5718', 'issn': ['0025-5718', '1088-6842'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310315719', 'host_organization_name': 'American Mathematical Society', 'host_organization_lineage': ['https://openalex.org/P4310315719'], 'host_organization_lineage_names': ['American Mathematical Society'], 'type': 'journal'}, 'license': 'public-domain', 'license_id': 'https://openalex.org/licenses/public-domain', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 22, 'referenced_works': ['https://openalex.org/W1492451367', 'https://openalex.org/W1576546137', 'https://openalex.org/W1582734821', 'https://openalex.org/W1963959271', 'https://openalex.org/W1966388474', 'https://openalex.org/W1971606961', 'https://openalex.org/W1994336408', 'https://openalex.org/W1995404822', 'https://openalex.org/W2064909895', 'https://openalex.org/W2065700840', 'https://openalex.org/W2075896209', 'https://openalex.org/W2118551467', 'https://openalex.org/W2138486270', 'https://openalex.org/W2143783905', 'https://openalex.org/W2495211843', 'https://openalex.org/W2505585705', 'https://openalex.org/W2562668947', 'https://openalex.org/W2577326798', 'https://openalex.org/W3149667697', 'https://openalex.org/W4232421488', 'https://openalex.org/W599756203', 'https://openalex.org/W603762250'], 'related_works': ['https://openalex.org/W816511862', 'https://openalex.org/W4313645560', 'https://openalex.org/W2948362504', 'https://openalex.org/W2799711503', 'https://openalex.org/W2643941443', 'https://openalex.org/W2382844561', 'https://openalex.org/W2238883956', 'https://openalex.org/W2083529992', 'https://openalex.org/W2047855059', 'https://openalex.org/W1480770706'], 'abstract_inverted_index': {'Reliable': [0], 'a': [1, 12, 20], 'posteriori': [2], 'error': [3], 'estimates': [4], 'without': [5], 'generic': [6], 'constants': [7], 'can': [8, 53], 'be': [9, 54, 76], 'obtained': [10], 'by': [11], 'comparison': [13], 'of': [14, 30, 41, 93], 'the': [15, 24, 48, 57, 72, 91], 'finite': [16], 'element': [17], 'solution': [18], 'with': [19, 80], 'feasible': [21], 'function': [22], 'for': [23, 38, 68], 'dual': [25], 'problem.': [26], 'A': [27], 'cheap': [28], 'computation': [29], 'such': [31, 50], 'functions': [32], 'via': [33], 'equilibration': [34, 49, 73], 'is': [35, 65], 'well': [36], 'known': [37], 'scalar': [39], 'equations': [40], 'second': [42], 'order.': [43], 'We': [44], 'simplify': [45], 'and': [46, 60], 'modify': [47], 'that': [51], 'it': [52], 'applied': [55], 'to': [56, 75], 'curl-curl': [58], 'equation': [59], 'edge': [61, 69], 'elements.': [62], 'The': [63], 'construction': [64], 'more': [66], 'involved': [67], 'elements': [70, 87], 'since': [71], 'has': [74], 'performed': [77], 'on': [78], 'subsets': [79], 'different': [81], 'dimensions.': [82], 'For': [83], 'this': [84], 'reason,': [85], 'Raviart–Thomas': [86], 'are': [88], 'extended': [89], 'in': [90], 'spirit': [92], 'distributions.': [94]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W1980377066', 'counts_by_year': [{'year': 2024, 'cited_by_count': 16}, {'year': 2023, 'cited_by_count': 19}, {'year': 2022, 'cited_by_count': 10}, {'year': 2021, 'cited_by_count': 19}, {'year': 2020, 'cited_by_count': 22}, {'year': 2019, 'cited_by_count': 13}, {'year': 2018, 'cited_by_count': 12}, {'year': 2017, 'cited_by_count': 10}, {'year': 2016, 'cited_by_count': 16}, {'year': 2015, 'cited_by_count': 9}, {'year': 2014, 'cited_by_count': 14}, {'year': 2013, 'cited_by_count': 13}, {'year': 2012, 'cited_by_count': 21}], 'updated_date': '2024-12-30T03:18:35.979964', 'created_date': '2016-06-24'}