{"id":"W4408909352","doi":"10.1137/1.9781611978285.ch4","title":"Chapter 4: Finite-element methods for elliptic differential equations in 1D","year":2025,"lang":"en","type":"book-chapter","venue":"Society for Industrial and Applied Mathematics eBooks","topic":"Advanced Numerical Methods in Computational Mathematics","field":"Engineering","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Memorial University of Newfoundland; University of Waterloo","funders":"","keywords":"Finite element method; Mathematics; Mathematical analysis; Physics; Thermodynamics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004191461,0.00124511,0.0009296608,0.002389809,0.0004575115,0.001663009,0.001240134,0.001661639,0.05004852],"category_scores_gemma":[0.0007188602,0.0007966995,0.0008874408,0.002555062,0.0005259339,0.0019407,0.001070038,0.002173152,0.02742735],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005188304,"about_ca_system_score_gemma":0.0007534231,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008757076,"about_ca_topic_score_gemma":0.001886847,"domain_scores_codex":[0.9996316,0.00003780873,0.00002278638,0.00005511378,0.000234286,0.00001838059],"domain_scores_gemma":[0.9997851,0.00007904531,0.00000878483,0.00002232209,0.00009205322,0.00001263974],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"not_applicable","study_design_scores_codex":[0.00002917017,0.0001369538,0.0001478501,0.002736586,0.00004486287,0.0000877033,0.0001967244,0.01890383,0.01074571,0.1072691,0.2049593,0.6547423],"study_design_scores_gemma":[0.000005579085,0.00002954775,0.0002134343,0.0006520793,0.00001445451,0.0002013186,0.00002631439,0.007017613,0.002299234,0.02546545,0.964051,0.00002396945],"study_design_candidate":"not_applicable","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.00174498,0.2106204,0.4688131,0.002247742,0.007645893,0.0003146998,0.00128704,0.002120189,0.305206],"genre_scores_gemma":[0.01066603,0.1834248,0.207596,0.001707704,0.003567323,0.0003830896,0.002469602,0.001532864,0.5886525],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.05004852,"threshold_uncertainty_score":0.167429,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09806236404224712,"score_gpt":0.3392759709367158,"score_spread":0.2412136068944687,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}