{"id":"W2111798853","doi":"10.1002/cnm.814","title":"Hamiltonian‐based error computations","year":2005,"lang":"en","type":"article","venue":"Communications in Numerical Methods in Engineering","topic":"Advanced Numerical Methods in Computational Mathematics","field":"Engineering","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University; University of Toronto","funders":"","keywords":"Computation; Hamiltonian (control theory); Applied mathematics; Mathematics; Lagrangian; Error analysis; Finite element method; Hamiltonian system; Hamiltonian optics; Invariant (physics); Algorithm; Mathematical optimization; Mathematical analysis; Covariant Hamiltonian field theory; Superintegrable Hamiltonian system; Physics","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":[0.001422453,0.0005446253,0.001013587,0.001382265,0.0006228731,0.001339067,0.001284693,0.0007274193,0.006631896],"category_scores_gemma":[0.006122894,0.0002683853,0.0005315262,0.0006089435,0.001541291,0.001391459,0.001905118,0.001029048,0.0008272121],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00080654,"about_ca_system_score_gemma":0.001147581,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003829603,"about_ca_topic_score_gemma":0.002714205,"domain_scores_codex":[0.9990276,0.0002436115,0.00005523028,0.00007345426,0.0005042831,0.00009579456],"domain_scores_gemma":[0.9972057,0.001158698,0.0002287198,0.0005284527,0.0007427763,0.0001356923],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.0001970749,0.00008833909,0.001753819,0.0001894711,0.00007759699,0.0001490552,0.0002022465,0.5771494,0.008486273,0.3362084,0.002211672,0.0732867],"study_design_scores_gemma":[0.00001335952,0.0000186538,0.0001811855,0.00001475975,0.000006404189,0.00001315296,0.0000183121,0.971657,0.00273564,0.02416203,0.001168444,0.00001106927],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.03793065,0.0001246941,0.9515022,0.0001260497,0.00009835821,0.00007684773,0.0001380314,0.0005369948,0.00946615],"genre_scores_gemma":[0.7377392,0.00016356,0.2529065,0.00009482573,0.00006841501,0.0001877587,0.0003357644,0.0004537317,0.008050215],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006631896,"threshold_uncertainty_score":0.02218598,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07868596881561873,"score_gpt":0.4272555776088257,"score_spread":0.348569608793207,"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."}}