{"id":"W2113152333","doi":"10.1145/353474.353482","title":"Accurate approximate solution of partial differential equations at off-mesh points","year":2000,"lang":"en","type":"article","venue":"ACM Transactions on Mathematical Software","topic":"Advanced Numerical Analysis Techniques","field":"Engineering","cited_by":8,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Collocation (remote sensing); Partial differential equation; Interpolation (computer graphics); Polygon mesh; Collocation method; Computer science; Domain (mathematical analysis); Mathematics; Set (abstract data type); Applied mathematics; Elliptic partial differential equation; Order of accuracy; Numerical analysis; Orthogonal collocation; Differential equation; Mathematical optimization; Algorithm; Numerical partial differential equations; Ordinary differential equation; Mathematical analysis; Geometry","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":[0.001391106,0.0005847589,0.001022328,0.0005523821,0.0005004365,0.001274996,0.001104274,0.001393784,0.001420426],"category_scores_gemma":[0.004759742,0.0003726096,0.0005907256,0.0006184752,0.001201042,0.001536006,0.001502144,0.001517512,0.000783223],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004855558,"about_ca_system_score_gemma":0.0007020352,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001122304,"about_ca_topic_score_gemma":0.001053003,"domain_scores_codex":[0.9990588,0.0002310411,0.00004786884,0.00008046256,0.0005184553,0.00006344167],"domain_scores_gemma":[0.9986552,0.0005991464,0.00009615078,0.0004202306,0.0002015587,0.00002764802],"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":[0.0001058312,0.00007624183,0.002412464,0.0003333433,0.00004591063,0.0004074921,0.0004209257,0.7513653,0.03300345,0.1122136,0.001478015,0.09813754],"study_design_scores_gemma":[0.00001165818,0.00003391708,0.0002521324,0.00002558113,0.000007984284,0.00009959879,0.00005435981,0.9702652,0.008758498,0.01644461,0.004035873,0.00001062234],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01742722,0.0001757192,0.9792765,0.00007163445,0.00003642722,0.00002555809,0.00002338057,0.0001804607,0.002783134],"genre_scores_gemma":[0.399649,0.0005802766,0.5940379,0.00009210883,0.00006152505,0.0001369925,0.0001879527,0.0001795299,0.005074714],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.001420426,"threshold_uncertainty_score":0.007357001,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01871754576201084,"score_gpt":0.2583963857301192,"score_spread":0.2396788399681083,"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."}}