{"doi":"10.1007/s40314-021-01426-5","title":"A posteriori error estimates for a multi-scale finite-element method","abstract":"<jats:title>Abstract</jats:title><jats:p>We are interested in the discretization of a diffusion problem with highly oscillating coefficient, by a multi-scale finite-element method (MsFEM). The objective of this method is to capture the multi-scale structure of the solution via local basis functions which contain the essential information on small scales. In this paper, we perform an <jats:italic>a posteriori</jats:italic> analysis of this discretization. The main result consists of building error indicators with respect to both small and large meshes used in this method. We present a numerical test in which the experiments are in good coherency with the results of analysis.</jats:p>","journal":"Computational and Applied Mathematics","year":2021,"id":22918,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":0,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":142533,"name":"Brahim Allam","orcid":null,"position":1,"is_corresponding":false},{"id":142534,"name":"Zoubida Mghazli","orcid":null,"position":2,"is_corresponding":false},{"id":142532,"name":"Khallih Ahmed Blal","orcid":null,"position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"base_score":0.0,"endowment":0.0,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"24259432","pmcid":null,"openalex_id":"https://openalex.org/W3157581885","authors":[],"funders":[],"total_grants":0,"fwci":0.0,"citation_percentile":0.08331002,"influential_citations":0,"citation_trend":[],"oa_status":"hybrid","license":"cc-by","oa_locations":[{"url":"https://link.springer.com/content/pdf/10.1007/s40314-021-01426-5.pdf","host_type":"journal"},{"url":"https://link.springer.com/content/pdf/10.1007/s40314-021-01426-5.pdf","host_type":"HYBRID"},{"url":"https://link.springer.com/content/pdf/10.1007/s40314-021-01426-5.pdf","host_type":"publisher"},{"url":"https://link.springer.com/article/10.1007/s40314-021-01426-5/fulltext.html","host_type":"publisher"},{"url":"https://doi.org/10.1007/s40314-021-01426-5","host_type":"journal"}],"fields_of_study":["Advanced Mathematical Modeling in Engineering","Advanced Numerical Methods in Computational Mathematics","Composite Material Mechanics","Computer Science","Engineering","Mathematics","Physics"],"mesh_terms":[],"keywords":["Discretization","A priori and a posteriori","Finite element method","Polygon mesh","Scale (ratio)","Applied mathematics","Discretization error","Basis (linear algebra)","Computer science","Mathematical optimization","Mathematics","Numerical analysis","Diffusion","Algorithm","Mathematical analysis","Geometry","Structural engineering","Physics"],"sdg_mappings":[],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-06-07T17:03:53.409169Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}