{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.006342488,0.001324153,0.00115605,0.001609532,0.0005458012,0.001634641,0.001279518,0.002180434,0.001380284],"category_scores_gemma":[0.01795623,0.0006177892,0.001281416,0.0005200726,0.002784977,0.002226976,0.002911069,0.002770235,0.000306605],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00118004,"about_ca_system_score_gemma":0.001159557,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001830092,"about_ca_topic_score_gemma":0.0008530116,"domain_scores_codex":[0.9987968,0.0004693879,0.0001024124,0.000144307,0.0004197146,0.00006738098],"domain_scores_gemma":[0.9898816,0.006997762,0.0009273441,0.0005016261,0.001433545,0.0002581055],"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":[0.0001098063,0.00005097564,0.001065098,0.0003481251,0.00006196944,0.0001142387,0.000242742,0.6627955,0.01038092,0.3111285,0.0005649953,0.01313718],"study_design_scores_gemma":[0.000002634564,0.00002498952,0.00008301646,0.00002930997,0.000004812648,0.00001684325,0.00001168554,0.9825487,0.001603784,0.01527215,0.000390065,0.00001191979],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01296335,0.0004541756,0.9844998,0.000328975,0.00004848773,0.00002882422,0.00004027729,0.0000547571,0.001581389],"genre_scores_gemma":[0.6312055,0.002351935,0.3578347,0.0003350525,0.0001767811,0.0003838934,0.0003833856,0.0002135689,0.00711514],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006342488,"threshold_uncertainty_score":0.03354269,"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."}}