{"id":"W4283785404","doi":"10.1016/j.camwa.2022.05.038","title":"Optimal error analysis of the spectral element method for the 2D homogeneous wave equation","year":2022,"lang":"en","type":"article","venue":"Computers & Mathematics with Applications","topic":"Advanced Numerical Methods in Computational Mathematics","field":"Engineering","cited_by":4,"is_retracted":false,"has_abstract":false,"ca_institutions":"Polytechnique Montréal","funders":"","keywords":"Mathematics; Spectral element method; Discretization; Mathematical analysis; Quadrilateral; Affine transformation; Diagonal; Quadrature (astronomy); Spectral method; Finite element method; Norm (philosophy); Legendre polynomials; Applied mathematics; Geometry; Mixed finite element method; 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004478721,0.0001647675,0.0003024211,0.0001166765,0.0003659732,0.00002236226,0.0005127194,0.00002086351,0.00002748861],"category_scores_gemma":[0.00003472192,0.00010944,0.0001974621,0.001320002,0.00006591525,0.00002711813,0.0001437153,0.0001578775,0.000001081036],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001343721,"about_ca_system_score_gemma":0.00002919895,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001109147,"about_ca_topic_score_gemma":0.000001334975,"domain_scores_codex":[0.9987354,0.00005635848,0.000452515,0.0001880838,0.000377811,0.0001897748],"domain_scores_gemma":[0.9963188,0.002671216,0.0002479263,0.0006259565,0.00009864951,0.00003746886],"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":[0.00000361197,0.00008530181,0.000004002417,0.00007071085,0.0006008024,1.178039e-7,0.000734482,0.9473624,0.0001357146,0.04299402,0.00008903015,0.007919817],"study_design_scores_gemma":[0.0001421779,0.00004084495,0.00006295959,0.000007094944,0.0008555574,0.00001074896,0.0003676345,0.969862,0.0004085826,0.02681759,0.001295426,0.0001293463],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.0009849654,0.00007244312,0.9967938,0.0002335328,0.00008588855,0.001539376,0.00008720806,0.00009641745,0.0001063514],"genre_scores_gemma":[0.03895513,0.000003893008,0.9588311,0.0000601845,0.00003965078,0.002024097,0.00002294671,0.00003760723,0.00002540771],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.03797017,"threshold_uncertainty_score":0.4462833,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0404305813843759,"score_gpt":0.3154295527491641,"score_spread":0.2749989713647882,"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."}}