{"doi":"10.1002/nme.999","title":"Moving particle finite element method with global smoothness","abstract":"<jats:title>Abstract</jats:title><jats:p>We describe a new version of the moving particle finite element method (MPFEM) that provides solutions within a <jats:italic>C</jats:italic><jats:sup>0</jats:sup> finite element framework. The finite elements determine the weighting for the moving partition of unity. A concept of ‘General Shape Function’ is proposed which extends regular finite element shape functions to a larger domain. These are combined with Shepard functions to obtain a smooth approximation. The Moving Particle Finite Element Method combines desirable features of finite element and meshfree methods. The proposed approach, in fact, can be interpreted as a ‘moving partition of unity finite element method’ or ‘moving kernel finite element method’. This method possesses the robustness and efficiency of the <jats:italic>C</jats:italic><jats:sup>0</jats:sup> finite element method while providing at least <jats:italic>C</jats:italic><jats:sup>1</jats:sup> continuity. Copyright © 2004 John Wiley &amp; Sons, Ltd.</jats:p>","journal":"International Journal for Numerical Methods in Engineering","year":2004,"id":24366,"datarank":1.489268848917193,"base_score":3.4339872044851463,"endowment":3.4339872044851463,"self_citation_contribution":0.515098080672772,"citation_network_contribution":0.9741707682444211,"self_endowment_contribution":0.515098080672772,"citer_contribution":0.9741707682444211,"corpus_percentile":null,"corpus_rank":null,"citation_count":30,"citer_count":22,"citers_with_citation_signal":20,"citers_with_endowment":20,"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":146423,"name":"Wing Kam Liu","orcid":null,"position":1,"is_corresponding":false},{"id":132794,"name":"Ted Belytschko","orcid":null,"position":2,"is_corresponding":false},{"id":146422,"name":"Su Hao","orcid":null,"position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"base_score":3.4339872044851463,"endowment":3.4339872044851463,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"24523987","pmcid":null,"openalex_id":"https://openalex.org/W2165887158","authors":[],"funders":[],"total_grants":0,"fwci":3.9089,"citation_percentile":0.92898948,"influential_citations":1,"citation_trend":[{"year":2013,"count":1},{"year":2014,"count":3},{"year":2017,"count":1},{"year":2020,"count":1},{"year":2024,"count":1}],"oa_status":"closed","license":"http://onlinelibrary.wiley.com/termsAndConditions#vor","oa_locations":[{"url":"https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1002%2Fnme.999","host_type":"publisher"},{"url":"https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.999","host_type":"publisher"},{"url":"https://doi.org/10.1002/nme.999","host_type":"journal"}],"fields_of_study":["Numerical methods in engineering","Geotechnical Engineering and Underground Structures","Fluid Dynamics Simulations and Interactions","Mathematics","Engineering"],"mesh_terms":[],"keywords":["Finite element method","Extended finite element method","Smoothed finite element method","Mixed finite element method","Partition of unity","Finite element limit analysis","hp-FEM","Boundary knot method","Mathematics","Diffuse element method","Discrete element method","Mathematical analysis","Applied mathematics","Mathematical optimization","Physics","Mechanics","Structural engineering","Engineering"],"sdg_mappings":[],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-06-07T22:15:15.534628Z","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":[]}