{"id":"W2555420911","doi":"10.1139/tcsme-2010-0013","title":"HAMILTONIAN AS ERROR INDICATOR IN THE <i>P</i>-VERSION OF FINITE ELEMENT METHOD","year":2010,"lang":"en","type":"article","venue":"Transactions of the Canadian Society for Mechanical Engineering","topic":"Numerical methods in engineering","field":"Engineering","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University; University of Toronto","funders":"","keywords":"Hamiltonian (control theory); Finite element method; Residual; Applied mathematics; Error analysis; Approximation error; Method of mean weighted residuals; Mathematics; Rate of convergence; Hamiltonian system; Polynomial; Mathematical optimization; Computer science; Algorithm; Mathematical analysis; Physics; Galerkin method","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":true,"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":[0.001708812,0.0003938008,0.0006450819,0.0005543475,0.0003570523,0.0008752621,0.001283491,0.001053125,0.001782532],"category_scores_gemma":[0.003588073,0.0002516835,0.0004360604,0.0004919593,0.001235693,0.001396609,0.001240743,0.001179988,0.0004260734],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003835566,"about_ca_system_score_gemma":0.0006870729,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002039775,"about_ca_topic_score_gemma":0.001261008,"domain_scores_codex":[0.9992123,0.0002654959,0.00004721898,0.00007492372,0.0003466384,0.00005350978],"domain_scores_gemma":[0.9986513,0.0006288748,0.0001157209,0.0002403716,0.0003119918,0.00005168744],"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":[0.0002963567,0.0001562037,0.003012935,0.0004780002,0.00009109067,0.0003253988,0.0002809754,0.617457,0.03479042,0.2269368,0.001573626,0.1146012],"study_design_scores_gemma":[0.000008609222,0.0000425098,0.0002460327,0.00001487523,0.000007351298,0.00003827571,0.00001579817,0.9869022,0.003925608,0.007859042,0.0009258045,0.00001378868],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01988058,0.0002754521,0.9762177,0.0001438386,0.00008467705,0.00003674299,0.00004767442,0.0002155516,0.003097653],"genre_scores_gemma":[0.5492432,0.0005835529,0.4408307,0.0001749776,0.0000986032,0.0001739961,0.0001699444,0.0005466475,0.008178439],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.002039775,"threshold_uncertainty_score":0.009037137,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01013401625256363,"score_gpt":0.2499405536438096,"score_spread":0.239806537391246,"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."}}