Conference: Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations

首席调查员(PI)和共同调查员于2012年5月9日至11日在诺克斯维尔田纳西大学举办了2012年约翰·H·巴雷特纪念讲座(www.math.utk.edu/~xfan/barrett/)。巴雷特讲座自1972年以来每年举行一次。每年都会选择一个不同的主题，代表田纳西大学数学系的研究兴趣。自1993年以来，这些讲座包括三次一小时的调查报告，由代表同一领域不同主题和方向的两到三名主要研究人员分别进行。2012年巴雷特讲座的主题是：“偏微分方程间断伽辽金有限元方法的最新发展”。2012年巴雷特讲座的主要演讲人是意大利帕维亚大学的佛朗哥·布雷齐和布朗大学的舒志旺。他们将分别就间断Galerkin有限元方法的最新发展发表三个一小时的综述讲座，分别侧重于内部惩罚和局部间断Galerkin方法。除主讲嘉宾外，十位主讲嘉宾还将就其中一场主讲的相关主题，以及间断伽辽金有限元方法在双曲守恒律和哈密顿-雅可比方程、对流扩散方程、浅水方程、多孔介质流动、弹性、高频波动方程和材料相变中的应用，进行一小时的演讲。此外，讲座还安排了一个海报环节，让与会者有机会介绍他们在这些领域的工作。巴雷特的讲座部分由田纳西大学的拨款资助，并经常得到国家科学基金会的额外资助。它们吸引了广泛的兴趣，除了来自诺克斯维尔和橡树岭国家实验室的教职员工和学生外，还有来自全国各地的40至60名参与者。它们代表了美国东南部为数不多的历史悠久的数学系列讲座之一。2012年巴雷特讲座的主要目的是通过深入的调查讲座和与该领域的主要研究人员的非正式讨论，向与会者介绍现代间断伽辽金有限元方法在各种科学/工程/工业应用中产生的偏微分方程组。其他目标是促进跨学科合作，特别是与田纳西大学工程学院和其他几个东南部机构的领域科学系和研究人员的合作，并产生一套关于这一主题的书面调查，组委会将努力以书籍的形式出版。向国家科学基金会申请的资金将用于为30名没有研究补助金的研究生、博士后和初级研究人员提供旅行和住宿方面的部分支持。

The principal investigator (PI) and Co-PIs organize the 2012 John H. Barrett Memorial Lectures in the University of Tennessee at Knoxville from May 9-11, 2012 (www.math.utk.edu/~xfeng/barrett/). The Barrett Lectures have been held annually since 1972. Each year a different topic is chosen, representing the research interests of the mathematics faculty of the University of Tennessee. Since 1993, the lectures have consisted of three one-hour survey talks by each of two or three leading researchers representing different themes and directions in a single field. The topic of the 2012 Barrett Lectures is: ``Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations". The main speakers of the 2012 Barrett Lectures are Franco Brezzi of University of Pavia(Italy) and Chi-Wang Shu of Brown University. Each of them will deliver three one-hour survey lectures on recent developments in discontinuous Galerkin finite element methods with respective emphases on interior penalty and local discontinuous Galerkin methods. In addition to the main speakers, ten speakers are also invited to give one-hour talks on topics related to one of the main lectures and on applications of discontinuous Galerkin finite element methods to hyperbolic conservation laws and Hamilton-Jacobi equations, convection-diffusion equations, shallow water equations, porous media flows, elasticity, high frequency wave equations, and materials phase transitions. Moreover, a poster session is also scheduled in the Lectures, giving the opportunity to those who attend the meeting to present their work in these areas.The Barrett Lectures are partly funded by a grant from the University of Tennessee and have often received additional support from the National Science Foundation. They attract wide interest, with an audience of between 40 and 60 participants from the whole country, in addition to faculty and students from Knoxville and the Oak Ridge National Laboratory. They represent one of the few long standing lecture series in mathematics in the southeastern United States. The main objective of the 2012 Barrett Lectures is to provide the participants with an exposition of modern discontinuous Galerkin finite element methods for partial differential equations arising from various scientific/engineering/industrial applications, through in-depth survey lectures and informal discussions with the leading researchers in the field. Additional goals are to foster interdisciplinary collaboration, particularly with researchers in the domain sciences departments and in the College of Engineering at the University of Tennessee and several other southeastern institutions, and to generate a set of written surveys in the subject, which the organizing committee will endeavor to have published in book form. The fund being requested from the NSF will be spent providing partial support towards travel and accommodation for thirty graduate students, postdocs, and junior researchers who do not have research grants.