{"id":"W4408909359","doi":"10.1137/1.9781611978285.ch8","title":"Chapter 8: Finite-element methods for elliptic partial differential equations","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; Elliptic partial differential equation; Mathematics; Partial differential equation; Mathematical analysis; Applied mathematics; 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":[0.0003952862,0.001145515,0.000828702,0.002171951,0.000451153,0.00145336,0.001132688,0.001490792,0.04281539],"category_scores_gemma":[0.0007000453,0.0006563766,0.0006944911,0.002267685,0.0004570653,0.001714848,0.0009247657,0.002089012,0.02710578],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004497249,"about_ca_system_score_gemma":0.0006927614,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007657789,"about_ca_topic_score_gemma":0.001648167,"domain_scores_codex":[0.9996296,0.00003581714,0.0000229325,0.00004935225,0.0002441405,0.00001812402],"domain_scores_gemma":[0.999765,0.00008324892,0.000008227633,0.00002276954,0.0001074658,0.00001329286],"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":[0.00002644709,0.0001278186,0.0001273695,0.002101076,0.00003876334,0.00008147272,0.0001886923,0.01135266,0.008763596,0.0948767,0.2050277,0.6772878],"study_design_scores_gemma":[0.000005872853,0.00002421234,0.0001988663,0.0005608861,0.00001348998,0.0001918767,0.00002802661,0.004932259,0.00220982,0.02412275,0.9676944,0.00001756456],"study_design_candidate":"not_applicable","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.001850611,0.2193674,0.4385112,0.002320747,0.006311583,0.0002635552,0.00114662,0.001996854,0.3282314],"genre_scores_gemma":[0.01159642,0.1808735,0.1821148,0.00136029,0.003192351,0.0003564295,0.002508764,0.001468976,0.6165285],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.04281539,"threshold_uncertainty_score":0.1432317,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1048112084709985,"score_gpt":0.3394772692466786,"score_spread":0.2346660607756802,"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."}}