{"id":"W4385685797","doi":"10.1007/s11075-023-01635-5","title":"Adaptive discontinuous Galerkin finite element methods for the Allen-Cahn equation on polygonal meshes","year":2023,"lang":"en","type":"article","venue":"Numerical Algorithms","topic":"Advanced Numerical Methods in Computational Mathematics","field":"Engineering","cited_by":14,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Calgary","funders":"Basic and Applied Basic Research Foundation of Guangdong Province; Natural Science Foundation of Shaanxi Province; National Natural Science Foundation of China; China Postdoctoral Science Foundation; CMG Reservoir Simulation Foundation","keywords":"Polygon mesh; Discretization; Finite element method; Mathematics; Discontinuous Galerkin method; Allen–Cahn equation; Curvature; Galerkin method; Backward Euler method; Mesh generation; Applied mathematics; Algorithm; Mathematical analysis; Geometry","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":[0.0004806817,0.0004115542,0.0005844499,0.0004901357,0.0005021103,0.0008340071,0.001447706,0.001209041,0.002082382],"category_scores_gemma":[0.003138718,0.0003427243,0.0004131211,0.0005754278,0.001154477,0.000908028,0.001375019,0.001546136,0.0003196577],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006002199,"about_ca_system_score_gemma":0.0007297317,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00461788,"about_ca_topic_score_gemma":0.004488591,"domain_scores_codex":[0.9996692,0.0001080852,0.0000137019,0.0000381448,0.0001477891,0.00002308015],"domain_scores_gemma":[0.9990512,0.0006604511,0.00005909874,0.00006470097,0.0001335751,0.00003100718],"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":[0.00008168028,0.00005988156,0.0007279341,0.0001445801,0.00002506956,0.0001223021,0.0002211984,0.8300226,0.006855026,0.1131517,0.00185825,0.04672981],"study_design_scores_gemma":[0.000005507096,0.000005173685,0.00003672198,0.000004608765,0.000001952542,0.00001260212,0.000009445305,0.9934785,0.0004368104,0.005061697,0.0009433972,0.00000353808],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01485662,0.0001821429,0.9806984,0.0001468051,0.0000739077,0.00003669914,0.00004791887,0.00008075762,0.003876745],"genre_scores_gemma":[0.4976996,0.0005943607,0.4878004,0.0001317393,0.0001158556,0.0002359543,0.0001929104,0.0002257258,0.01300337],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.00461788,"threshold_uncertainty_score":0.009181976,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09488628490794512,"score_gpt":0.3830505601114902,"score_spread":0.2881642752035452,"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."}}