报告题目 (Title)：生物数学模型有限元方法的超收敛分析（Super-convergence Analysis of FEMs for the Biological Models）
报告人 (Speaker)： 石东洋 二级教授（郑州大学）
报告时间 (Time)：2023年10月23日(周一) 14:00
报告地点 (Place)：F309
邀请人(Inviter)：李新祥
报告摘要：Abstract：This talk considers the superconvergence analysis of two types of the Biological models with FEMs. For the second-order prey-predator equation, the energy stabilities of BE、BDF2 and CN schemes are proved, which leads to the unconditional superconvergence estimates. Furthermore, for the time-fractional case, a novel high accuracy estimate for the CNQ1rot element is certified by the Bramble-Hilbert (B-H) lemma. Moreover, the above estimate is also extended to anisotropic meshes. Then, the energy stability of L1 schemes is demonstrated, too. For the fourth-order bi-flux equation, a novel important property of high accuracy for the P1 element is presented by the B-H lemma. The energy stabilities and unconditional superconvergence results for the BE and CN schemes are also obtained. Some numerical tests are carried out to confirm the theoretical analysis.