This book aims to provide a comprehensive study of the mathematical theory of the vortex method, from its origins in the 1930s, through the developments of the '70s when the use of computers made advanced research possible, to current work on this subject in China and elsewhere. The five chapters treat vortex methods for the Euler and Navier-Stokes equations; mathematical theory for incompressible flows; convergence of vortex methods for the Euler equations; convergence of viscosity splitting; and convergence of the random vortex method. Audience: This volume will be of interest to researchers and graduate students of applied mathematics, scientists in fluid dynamics, and aviation engineers.

The International Symposium on Computational & Applied PDEs was held at Zhangjiajie National Park of China from July 1-7, 2001. The main goal of this conference is to bring together computational, applied and pure mathematicians on different aspects of partial differential equations to exchange ideas and to promote collaboration. Indeed, it attracted a number of leading scientists in computational PDEs including Doug Arnold (Minnesota), Jim Bramble (Texas A & M), Achi Brandt (Weizmann), Franco Brezzi (Pavia), Tony Chan (UCLA), Shiyi Chen (John Hopkins), Qun Lin (Chinese Academy of Sciences), Mitch Luskin (Minnesota), Tom Manteuffel (Colorado), Peter Markowich (Vienna), Mary Wheeler (Texas Austin) and Jinchao Xu (Penn State); in applied and theoretical PDEs including Weinan E (Princeton), Shi Jin (Wisconsin), Daqian Li (Fudan) and Gang Tian (MIT). It also drew an international audience of size 100 from Austria, China, Germany, Hong Kong, Iseael, Italy, Singapore and the United States. The conference was organized by Yunqing Huang of Xiangtan University, Jinchao Xu of Penn State University, and Tony Chan of UCLA through ICAM (Institute for Computational and Applied Mathematics) of Xiangtan university which was founded in January 1997 and directed by Jinchao Xu. The scientific committee of this conference consisted of Randy Bank of UCSD, Tony Chan of UCLA, K. C.

The International Symposium on Computational & Applied PDEs was held at Zhangjiajie National Park of China from July 1-7, 2001. The main goal of this conference is to bring together computational, applied and pure mathematicians on different aspects of partial differential equations to exchange ideas and to promote collaboration. Indeed, it attracted a number of leading scientists in computational PDEs including Doug Arnold (Minnesota), Jim Bramble (Texas A & M), Achi Brandt (Weizmann), Franco Brezzi (Pavia), Tony Chan (UCLA), Shiyi Chen (John Hopkins), Qun Lin (Chinese Academy of Sciences), Mitch Luskin (Minnesota), Tom Manteuffel (Colorado), Peter Markowich (Vienna), Mary Wheeler (Texas Austin) and Jinchao Xu (Penn State); in applied and theoretical PDEs including Weinan E (Princeton), Shi Jin (Wisconsin), Daqian Li (Fudan) and Gang Tian (MIT). It also drew an international audience of size 100 from Austria, China, Germany, Hong Kong, Iseael, Italy, Singapore and the United States. The conference was organized by Yunqing Huang of Xiangtan University, Jinchao Xu of Penn State University, and Tony Chan of UCLA through ICAM (Institute for Computational and Applied Mathematics) of Xiangtan university which was founded in January 1997 and directed by Jinchao Xu. The scientific committee of this conference consisted of Randy Bank of UCSD, Tony Chan of UCLA, K. C.

"As its name indicates, in the infinite element method the underlying domain is divided into infinitely many pieces. This leads to a system of infinitely many equations for infinitely many unknowns; but these can be reduced by analytical techniques to a finite system when some sort of scaling is present in the original problem. The simplest illustrative example, described carefully at the beginning of the first chapter of the book, is the solution of the Dirichlet problem in the exterior of some polygon. The exterior is subdivided into annular regions by a sequence of geometrically expanding images of the given polygon; these annuli are then further subdivided. The resulting variational equations take the form of a block tridiagonal Toeplitz matrix, with an inhomogeneous term in the zero component. Various efficient methods are described for solving such systems of equations. ... The infinfte element method is, whereever applicable, an elegant and efficient approach to solving problems in physics and engineering. Professor Yings welcome book makes it available to the community of numerical analysts and computational scientists. " (From the Preface by Peter D. Lax)Die Infinite Elemente Methode wird hauptsachlich bei der Berechnung singularer Loesungen partieller Differentialgleichungen und bei deren Loesung von Gleichungen auf unbeschrankten Gebieten angewandt. In dem Buch wird ein spezielles numerisches Verfahren vorgestellt, das bisher noch relativ unbekannt geblieben ist.