This book treats Modelling of CFD problems, Numerical tools for PDE, and Scientific Computing and Systems of ODE for Epidemiology, topics that are closely related to the scientific activities and interests of Prof. William Fitzgibbon, Prof. Yuri Kuznetsov, and Prof. O. Pironneau, whose outstanding achievements are recognised in this volume. It contains 20 contributions from leading scientists in applied mathematics dealing with partial differential equations and their applications to engineering, ab-initio chemistry and life sciences. It includes the mathematical and numerical contributions to PDE for applications presented at the ECCOMAS thematic conference "Contributions to PDE for Applications" held at Laboratoire Jacques Louis Lions in Paris, France, August 31- September 1, 2015, and at the Department of Mathematics, University of Houston, Texas, USA, February 26-27, 2016. This event brought together specialists from universities and research institutions who are developing or applying numerical PDE or ODE methods with an emphasis on industrial and societal applications. This volume is of interest to researchers and practitioners as well as advanced students or engineers in applied and computational mathematics. All contributions are written at an advanced scientific level with no effort made by the editors to make this volume self-contained. It is assumed that the reader is a specialist already who knows the basis of this field of research and has the capability of understanding and appreciating the latest developments in this field.

The present volume is comprised of contributions solicited from invitees to conferences held at the University of Houston, University of Jyv] askyl] a, and Xi'an Jiaotong University honoring the 70th birthday of Professor Roland Glowinski. Although scientists convened on three di?erent continents, the - itors prefer to view the meetings as single event. The three locales signify the fact Roland has friends, collaborators and admirers across the globe. The contents span a wide range of topics in contemporary applied mathematics rangingfrompopulationdynamics, to electromagnetics, to ?uidmechanics, to the mathematics of ?nance among others. However, they do not fully re?ect the breath and diversity of Roland's scienti?c interest. His work has always been at the intersection mathematics and scienti?c computing and their - plication to mechanics, physics, aeronautics, engineering sciences and more recently biology. He has made seminal contribution in the areas of methods for science computation, ?uid mechanics, numerical controls for distributed parameter systems, and solid and structural mechanics as well as shape - timization, stellar motion, electron transport, and semiconductor modeling. Two central themes arise from the corpus of Roland's work. The ?rst is that numerical methods should take advantage of the mathematical properties of themodel. Theyshouldbeportableandcomputablewithcomputingresources of the foreseeable future as well as with contemporary resources. The second theme is that whenever possible one should validate numerical with expe- mental data. The volume is written at an advanced scienti?c level and no e?ort has been made to make it self contained."

The present volume is comprised of contributions solicited from invitees to conferences held at the University of Houston, University of Jyv] askyl] a, and Xi'an Jiaotong University honoring the 70th birthday of Professor Roland Glowinski. Although scientists convened on three di?erent continents, the - itors prefer to view the meetings as single event. The three locales signify the fact Roland has friends, collaborators and admirers across the globe. The contents span a wide range of topics in contemporary applied mathematics rangingfrompopulationdynamics, to electromagnetics, to ?uidmechanics, to the mathematics of ?nance among others. However, they do not fully re?ect the breath and diversity of Roland's scienti?c interest. His work has always been at the intersection mathematics and scienti?c computing and their - plication to mechanics, physics, aeronautics, engineering sciences and more recently biology. He has made seminal contribution in the areas of methods for science computation, ?uid mechanics, numerical controls for distributed parameter systems, and solid and structural mechanics as well as shape - timization, stellar motion, electron transport, and semiconductor modeling. Two central themes arise from the corpus of Roland's work. The ?rst is that numerical methods should take advantage of the mathematical properties of themodel. Theyshouldbeportableandcomputablewithcomputingresources of the foreseeable future as well as with contemporary resources. The second theme is that whenever possible one should validate numerical with expe- mental data. The volume is written at an advanced scienti?c level and no e?ort has been made to make it self contained."

This book treats Modelling of CFD problems, Numerical tools for PDE, and Scientific Computing and Systems of ODE for Epidemiology, topics that are closely related to the scientific activities and interests of Prof. William Fitzgibbon, Prof. Yuri Kuznetsov, and Prof. O. Pironneau, whose outstanding achievements are recognised in this volume. It contains 20 contributions from leading scientists in applied mathematics dealing with partial differential equations and their applications to engineering, ab-initio chemistry and life sciences. It includes the mathematical and numerical contributions to PDE for applications presented at the ECCOMAS thematic conference "Contributions to PDE for Applications" held at Laboratoire Jacques Louis Lions in Paris, France, August 31- September 1, 2015, and at the Department of Mathematics, University of Houston, Texas, USA, February 26-27, 2016. This event brought together specialists from universities and research institutions who are developing or applying numerical PDE or ODE methods with an emphasis on industrial and societal applications. This volume is of interest to researchers and practitioners as well as advanced students or engineers in applied and computational mathematics. All contributions are written at an advanced scientific level with no effort made by the editors to make this volume self-contained. It is assumed that the reader is a specialist already who knows the basis of this field of research and has the capability of understanding and appreciating the latest developments in this field.