一、報(bào)告題目

The Interior Penalty Virtual Element Method for the Biharmonic Problem

二、報(bào)告人

趙紀(jì)坤 副教授

三、報(bào)告時(shí)間

12月18日下午16：30

四、報(bào)告地點(diǎn)

蓮花街校區(qū)惟德樓315會(huì)議室

五、報(bào)告摘要

We present an interior penalty virtual element method (IPVEM) for solving the biharmonic problem on polygonal meshes. An H1-nonconforming virtual element is constructed with the same degrees of freedom as the usual H1-conforming virtual element, but it locally has H2-regularity on each polygon in meshes. To enforce the C1 continuity, an interior penalty formulation is adopted. Hence, this new numerical scheme can be regarded as a combination of the virtual element space and discontinuous Galerkin scheme. Compared with the existing methods, this approach has some advantages in reducing the degree of freedom and capability of handling hanging nodes. The well-posedness and optimal convergence of the IPVEM are proven in a mesh-dependent norm. Some numerical results are presented to verify the theoretical results.

六、個(gè)人簡(jiǎn)介

趙紀(jì)坤，鄭州大學(xué)副教授。2016年獲鄭州大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院博士學(xué)位，并留校工作至今。主要研究領(lǐng)域包括有限元方法，穩(wěn)定化方法，虛擬元方法等。近年來(lái)，在虛擬元方法的單元構(gòu)造和理論研究方面取得了一些重要的成果，如H(curl^2)協(xié)調(diào)元、H^2非協(xié)調(diào)元、無(wú)散度非協(xié)調(diào)Stokes單元等虛擬單元的構(gòu)造以及內(nèi)罰虛擬元方法?，F(xiàn)主持國(guó)家自然科學(xué)基金面上項(xiàng)目1項(xiàng)。已主持完成國(guó)家自然科學(xué)基金青年基金1項(xiàng)、河南省自然科學(xué)基金面上項(xiàng)目1項(xiàng)和河南省高等學(xué)校重點(diǎn)科研項(xiàng)目1項(xiàng)，并以第一作者或通訊作者在國(guó)際SCI期刊發(fā)表學(xué)術(shù)論文20余篇，其中包括SIAM J Numer Anal, Math Comput, Math Models Methods Appl Sci, J Comput Phys, Comput Methods Appl Mech Engrg, IMA J Numer Anal等期刊。

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數(shù)學(xué)與統(tǒng)計(jì)學(xué)院
2024年12月17日