[10-11] 哈尔滨工业大学刘文杰副教授学术报告
报告题目: Polynomial approximation of singular functions in new fractional spaces
报 告 人: 刘文杰(哈尔滨工业大学)
报告时间: 2022年10月11日(周二),14:00-17:30
腾讯会议:https://meeting.tencent.com/dm/zvlcQJ6CnkTO
会议ID:914 522 018
报告摘要:In this talk, we introduce a new theoretical framework built upon fractional spaces for optimal error estimates of orthogonal polynomial approximations to functions with limited regularity. It naturally arises from exact representations of orthogonal polynomial expansion coefficients. Here, the essential pieces of the puzzle for the error analysis include (i) fractional integration by parts (under the weakest possible conditions), (ii) fractional taylor formula, (iii) generalised Gegenbauer functions of fractional degree (GGF-Fs): a new family of special functions with notable fractional calculus properties, and (iv) asymptotic formulas or uniform upper bounds of GGF-Fs. Finallywe introduce the hypothesis of Babuska and Hakula.
专家简介:刘文杰,男,哈尔滨工业大学数学学院副教授,博士研究生导师。曾在新加坡南洋理工大学做Research Fellow。主要研究谱方法及其应用、多项式逼近理论、奇异性问题的hp有限元方法等。获得中国博士后科学基金面上项目、国家自然科学基金青年项目和面上项目的资助。在Mathematics of Computation、Journal of Approximation Theory、Journal of Computational Physics等国际著名期刊发表SCI论文19篇。
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[10-13] 中国科学院数学与系统科学研究院周向宇院士学术报告
北京师范大学许孝精教授短期课程 | Theory on Well-posed of Boussinesq equations