A New Framework for the Stability Analysis of Perturbed Saddle-point Problems and Applications

报告题目：A New Framework for the Stability Analysis of Perturbed Saddle-point Problems and Applications

报告人：洪庆国（宾州州立大学）

报告时间：2023年6月12日14:00-16:00

报告地点：海纳苑2幢203

报告摘要：This talk provides a new abstract stability result for perturbed saddle-point problems which is based on a proper norm fitting. We derive the stability condition according to Babuska’s theory from a small inf-sup condition, similar to the famous Ladyzhenskaya-Babuska-Brezzi (LBB) condition, and the other standard assumptions in Brezzi’s theory under the resulting combined norm. The proposed framework allows to split the norms into proper seminorms and not only results in simpler (shorter) proofs of many stability results but also guides the construction of parameter robust norm-equivalent preconditioners. These benefits are demonstrated with several examples arising from different formulations of Biot’s model of consolidation.

报告人简介：洪庆国，博士，美国宾州州立大学Assistant  Research Professor，曾先后在奥地利科学院Radon研究所(RICAM)，德国Duisburg-Essen University, 美国宾州州立大学从事博士后研究，研究兴趣包括快速迭代法、间断有限元方法、机器学习等，在SIAM J. Numer.  Anal.,  Math. Comp.,  Numer. Math.,  J. Comput. Phys., Comput. Methods Appl. Mech. Engrg.，Math. Models Methods Appl. Sci.和Sci. China Math. 等国内外高水平期刊发表了诸多论文。