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伟德线上平台、所2021年系列學術活動(第66場):宋倫繼 教授 蘭州大學

發表于: 2021-06-10   點擊: 

報告題目:A relaxed weak Galerkin method for elliptic interface problems with low regularity

報告人:宋倫繼 教授 蘭州大學數學與統計學院

報告時間:2021年6月19日 10:30-11:30

報告地點:騰訊會議 會議 ID:877 874 999 會議密碼:0619

校内聯系人:柴世民 chaism@jlu.edu.cn


報告摘要:A new relaxed weak Galerkin (WG) method has been proposed for second order elliptic interface problems with low regularity solutions. We generalize the stabilizer from the weak Galerkin method based on a new relaxation index $\beta$, which can be tuned by the regularity of solution. The relaxed stabilization gives rise to considerable flexibility in treating weak continuity along interior element edges and interface edges. For solutions in Sobolev space $W^{l+1,p}$, with l≥0 and $p\in(1,2]$ rather than the usual case $p=2$, we derive convergence orders of the new WG method in the energy and $L^p$ norms under some regularity assumptions of the solution and an optimal selection of $\beta=1+\frac{4}{p}−p $ can be given in the energy norm. The stabilized WG method can be easily implemented without requiring any sufficiently large penalty factor. We will also introduce a new over-penalized weak Galerkin method and its applications.


報告人簡介:宋倫繼,蘭州大學數學與統計學院教授、應用數學博士、美國阿拉巴馬大學生物數學與高性能計算博士後,2020年首批國家一流本科課程負責人。從事非線性橢圓、抛物型偏微分方程的間斷Galerkin方法數值理論和計算、無界區域高頻時諧波散射問題高精度算法研究、間斷類型有限元解的PPR 梯度恢複技術等。在J. Comput. Phys., J. Sci. Comput., Appl. Numer. Math.等國内外學術期刊發表學術論文近30篇。主持國家自然科學青年基金、天元數學基金、省級項目、中央高校基本科研項目等6項。


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