A class of finite element methods, the Discontinuous Galerkin Methods (DGM), has been under rapid development recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simula tion, turbomachinery, turbulent flows, materials processing, MHD and plasma simulations, and image processing. While there has been a lot of interest from mathematicians, physicists and engineers in DGM, only scattered information is available and there has been no prior effort in organizing and publishing the existing volume of knowledge on this subject. In May 24-26, 1999 we organized in Newport (Rhode Island, USA), the first international symposium on DGM with equal emphasis on the theory, numerical implementation, and applications. Eighteen invited speakers, lead ers in the field, and thirty-two contributors presented various aspects and addressed open issues on DGM. In this volume we include forty-nine papers presented in the Symposium as well as a survey paper written by the organiz ers. All papers were peer-reviewed. A summary of these papers is included in the survey paper, which also provides a historical perspective of the evolution of DGM and its relation to other numerical methods. We hope this volume will become a major reference in this topic. It is intended for students and researchers who work in theory and application of numerical solution of convection dominated partial differential equations. The papers were written with the assumption that the reader has some knowledge of classical finite elements and finite volume methods."

This is the thirteenth issue (Vol. 7, No. 1, July 2019) of the Notices of the International Congress of Chinese Mathematicians (or ICCM Notices, for short), the official periodical of the ICCM organization. This special issue honors Shing-Tung Yau on the occasion of his 70th birthday. Published semi-annually, the Notices bring news, research, and presentation of various perspectives, relevant to Chinese mathematics development and education. Readers of the Notices will find research papers on various topics by prominent experts from around the world, interesting and timely articles on current applications and trends, biographical and historical essays, profiles of important institutions of research and learning, and more.

This is the eighteenth issue (Vol. 9, No. 2, December 2021 of the Notices of the International Congress of Chinese Mathematicians (or ICCM Notices, for short), the official periodical of the ICCM organization. Published semi-annually, the Notices bring news, research, and presentation of various perspectives, relevant to Chinese mathematics development and education. Readers of the Notices will find research papers on various topics by prominent experts from around the world, interesting and timely articles on current applications and trends, biographical and historical essays, profiles of important institutions of research and learning, and more.

This is the seventeenth issue (Vol. 9, No. 1, July 2021 of the Notices of the International Congress of Chinese Mathematicians (or ICCM Notices, for short), the official periodical of the ICCM organization. Published semi-annually, the Notices bring news, research, and presentation of various perspectives, relevant to Chinese mathematics development and education. Readers of the Notices will find research papers on various topics by prominent experts from around the world, interesting and timely articles on current applications and trends, biographical and historical essays, profiles of important institutions of research and learning, and more.

This is the twelfth issue (Vol. 6, No. 2, December 2018) of the Notices of the International Congress of Chinese Mathematicians (or ICCM Notices, for short), the official periodical of the ICCM organization. Published semi-annually, the Notices bring news, research, and presentation of various perspectives, relevant to Chinese mathematics development and education. Readers of the Notices will find research papers on various topics by prominent experts from around the world, interesting and timely articles on current applications and trends, biographical and historical essays, profiles of important institutions of research and learning, and more.

Handbook on Numerical Methods for Hyperbolic Problems: Applied and Modern Issues details the large amount of literature in the design, analysis, and application of various numerical algorithms for solving hyperbolic equations that has been produced in the last several decades. This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and become familiar with their relative advantages and limitations.

This is the fifteenth issue (Vol. 8, No. 1, July 2020) of the Notices of the International Congress of Chinese Mathematicians (or ICCM Notices, for short), the official periodical of the ICCM organization.Published semi-annually, the Notices bring news, research, and presentation of various perspectives, relevant to Chinese mathematics development and education. Readers of the Notices will find research papers on various topics by prominent experts from around the world, interesting and timely articles on current applications and trends, biographical and historical essays, profiles of important institutions of research and learning, and more.

Handbook of Numerical Methods for Hyperbolic Problems explores the changes that have taken place in the past few decades regarding literature in the design, analysis and application of various numerical algorithms for solving hyperbolic equations. This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and readily understand their relative advantages and limitations.

This book contains an expanded and smoothed version of lecture notes delivered by the authors at the Advanced School on Numerical Solutions of Partial Di?- ential Equations: New Trends and Applications, which took place at the Centre de Recerca Matem atica (CRM) in Bellaterra (Barcelona) from November 15th to 22nd, 2007. The book has three parts. The ?rst part, by Silvia Bertoluzza and Silvia Falletta, is devoted to the use of wavelets to derive some new approaches in the numerical solution of PDEs, showing in particular how the possibility of wr- ing equivalent norms for the scale of Besov spaces allows to write down some new methods.Thesecondpart, byGiovanniRusso, providesanoverviewofthemodern finite-volume and finite-difference shock-capturing schemes for systems of cons- vationandbalancelaws, with emphasisingiving auni?ed viewofsuchschemesby identifying the essential aspects of their construction. In the last part Chi-Wang Shugivesageneralintroductionto thediscontinuousGalerkinmethods forsolving some classes of PDEs, discussing cell entropy inequalities, nonlinear stability and error estimates. The school that originated these notes was born with the objective of p- viding an opportunity for PhD students, recent PhD doctorates and researchers in general in ?elds of applied mathematics and engineering to catch up with - portant developments in the ?elds and/or to get in touch with state-of-the-art numerical techniques that are not covered in usual courses at graduate leve

The year 2018 marked the 75th anniversary of the founding of Mathematics of Computation, one of the four primary research journals published by the American Mathematical Society and the oldest research journal devoted to computational mathematics. To celebrate this milestone, the symposium “Celebrating 75 Years of Mathematics of Computation” was held from November 1–3, 2018, at the Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island. The sixteen papers in this volume, written by the symposium speakers and editors of the journal, include both survey articles and new contributions. On the discrete side, there are four papers covering topics in computational number theory and computational algebra. On the continuous side, there are twelve papers covering topics in machine learning, high dimensional approximations, nonlocal and fractional elliptic problems, gradient flows, hyperbolic conservation laws, Maxwell's equations, Stokes's equations, a posteriori error estimation, and iterative methods. Together they provide a snapshot of significant achievements in the past quarter century in computational mathematics and also in important current trends.

This is the fourteenth issue (Vol. 7, No. 2, December 2019) of the Notices of the International Congress of Chinese Mathematicians (or ICCM Notices, for short), the official periodical of the ICCM organization. Published semi-annually, the Notices bring news, research, and presentation of various perspectives, relevant to Chinese mathematics development and education. Readers of the Notices will find research papers on various topics by prominent experts from around the world, interesting and timely articles on current applications and trends, biographical and historical essays, profiles of important institutions of research and learning, and more.

This is the tenth issue (Vol. 5, No. 2, December 2017) of the Notices of the International Congress of Chinese Mathematicians (or ICCM Notices, for short), the official periodical of the ICCM organization. Published semi-annually, the Notices bring news, research, and presentation of various perspectives, relevant to Chinese mathematics development and education. Readers of the Notices will find research papers on various topics by prominent experts from around the world, interesting and timely articles on current applications and trends, biographical and historical essays, profiles of important institutions of research and learning, and more.

This is the sixth issue (December 2015) of the Notices of the International Congress of Chinese Mathematicians (or ICCM Notices, for short), the official periodical of the ICCM organization. Published semi-annually, the Notices bring news, research, and presentation of various perspectives, relevant to Chinese mathematics development and education. Readers of the Notices will find research papers on various topics by prominent experts from around the world, interesting and timely articles on current applications and trends, biographical and historical essays, profiles of important institutions of research and learning, and more.

This is the fifth issue (July 2015) of the Notices of the International Congress of Chinese Mathematicians (or ICCM Notices, for short), the official periodical of the ICCM organization. Published semi-annually, the Notices bring news, research, and presentation of various perspectives, relevant to Chinese mathematics development and education. Readers of the Notices will find research papers on various topics by prominent experts from around the world, interesting and timely articles on current applications and trends, biographical and historical essays, profiles of important institutions of research and learning, and more.

This is the fourth issue (December 2014) of the Notices of the International Congress of Chinese Mathematicians (or ICCM Notices, for short), the official periodical of the ICCM organization. Published semi-annually, the Notices bring news, research, and presentation of various perspectives, relevant to Chinese mathematics development and education. Readers of the Notices will find research papers on various topics by prominent experts from around the world, interesting and timely articles on current applications and trends, biographical and historical essays, profiles of important institutions of research and learning, and more.

International Press of Boston is pleased to announce publication of the third issue (July 2014) of its all-new Notices of the International Congress of Chinese Mathematicians (or ICCM Notices, for short), the official periodical of the ICCM organization. The ICCM Notices brings news, research, and presentation of various perspectives, relevant to Chinese mathematics development and education. It is published semi-annually. The ICCM Notices will be of interest to all people-whether of Chinese background or not-who are interested in following Chinese mathematics.

International Press of Boston is pleased to announce publication of the second issue (December 2013) of its all-new Notices of the International Congress of Chinese Mathematicians (or ICCM Notices, for short), the official periodical of the ICCM organization. The ICCM Notices brings news, research, and presentation of various perspectives, relevant to Chinese mathematics development and education. It will be published semi-annually. The ICCM Notices will be of interest to all people-whether of Chinese background or not-who are interested in following Chinese mathematics.

International Press of Boston is pleased to announce publication of the first issue (July 2013) of its all-new Notices of the International Congress of Chinese Mathematicians (or ICCM Notices, for short), the official periodical of the ICCM organization. The ICCM Notices brings news, research, and presentation of various perspectives, relevant to Chinese mathematics development and education. It will be published semi-annually. The ICCM Notices will be of interest to all people-whether of Chinese background or not-who are interested in following Chinese mathematics.

This book captures the state-of-the-art in the field of Strong Stability Preserving (SSP) time stepping methods, which have significant advantages for the time evolution of partial differential equations describing a wide range of physical phenomena. This comprehensive book describes the development of SSP methods, explains the types of problems which require the use of these methods and demonstrates the efficiency of these methods using a variety of numerical examples. Another valuable feature of this book is that it collects the most useful SSP methods, both explicit and implicit, and presents the other properties of these methods which make them desirable (such as low storage, small error coefficients, large linear stability domains). This book is valuable for both researchers studying the field of time-discretizations for PDEs, and the users of such methods.