{"id":"W2012240233","doi":"10.1615/int.j.uncertaintyquantification.2014007972","title":"SOME A PRIORI ERROR ESTIMATES FOR FINITE ELEMENT APPROXIMATIONS OF ELLIPTIC AND PARABOLIC LINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS","year":2014,"lang":"en","type":"article","venue":"International Journal for Uncertainty Quantification","topic":"Probabilistic and Robust Engineering Design","field":"Decision Sciences","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada; Canada Research Chairs","keywords":"Mathematics; Stochastic partial differential equation; Superconvergence; Finite element method; Elliptic partial differential equation; Sobolev space; Partial differential equation; Parabolic partial differential equation; Discretization; Applied mathematics; A priori and a posteriori; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":true,"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":["metaresearch"],"consensus_categories":[],"category_scores_codex":[0.001945173,0.0001532774,0.0002739709,0.0003417889,0.0002798728,0.0002262315,0.0005104596,0.00007138874,0.00002566419],"category_scores_gemma":[0.0120072,0.0001198054,0.0001612696,0.0001378816,0.0001105529,0.0002840565,0.00004064303,0.0001062502,0.000008863785],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006439014,"about_ca_system_score_gemma":0.0001044364,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006337246,"about_ca_topic_score_gemma":0.000004042972,"domain_scores_codex":[0.9976104,0.00007283028,0.001030031,0.0003090986,0.0007511656,0.0002264539],"domain_scores_gemma":[0.9931242,0.004494556,0.0006475748,0.0002340978,0.001391613,0.0001079997],"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":[0.000179189,0.0001353085,0.00003982099,0.0000197931,0.00009669703,1.054465e-7,0.0003380928,0.6781334,0.002874144,0.3102215,0.0002511489,0.007710821],"study_design_scores_gemma":[0.0008145756,0.00013118,0.000350914,0.00004810066,0.00006904478,0.000005498085,0.00009518837,0.9003997,0.0005188192,0.09652272,0.0009242287,0.0001199573],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01508622,0.0001132363,0.9812875,0.001107414,0.00165052,0.0005765375,0.0001518631,0.00002313271,0.000003538246],"genre_scores_gemma":[0.975205,0.00001182874,0.02364217,0.00002870742,0.0006578283,0.0001528108,0.0001236513,0.00001533501,0.0001626467],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.9601188,"threshold_uncertainty_score":0.9963151,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1271159786429568,"score_gpt":0.3925801994975809,"score_spread":0.2654642208546242,"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."}}