As a satellite conference of the 1998 International Mathematical Congress and part of the celebration of the 650th anniversary of Charles University, the Partial Differential Equations Theory and Numerical Solution conference was held in Prague in August, 1998. With its rich scientific program, the conference provided an opportunity for almost 200 participants to gather and discuss emerging directions and recent developments in partial differential equations (PDEs).This volume comprises the Proceedings of that conference. In it, leading specialists in partial differential equations, calculus of variations, and numerical analysis present up-to-date results, applications, and advances in numerical methods in their fields. Conference organizers chose the contributors to bring together the scientists best able to present a complex view of problems, starting from the modeling, passing through the mathematical treatment, and ending with numerical realization. The applications discussed include fluid dynamics, semiconductor technology, image analysis, motion analysis, and optimal control.The importance and quantity of research carried out around the world in this field makes it imperative for researchers, applied mathematicians, physicists and engineers to keep up with the latest developments. With its panel of international contributors and survey of the recent ramifications of theory, applications, and numerical methods, Partial Differential Equations: Theory and Numerical Solution provides a convenient means to that end.

The book is the Proceedings of the Conference ENUMATH 2003, the 5th European Conference on Numerical Mathematics, concerned with most recent achievements in scientific computing, computational mathematics, numerical analysis and their applications. These proceedings contain a selection of invited plenary lectures, papers presented in minisymposia and contributed papers. All contributions to these proceedings have been reviewed by members of the Scientific Committee. Attention is paid to theoretical aspects of new numerical techniques and algorithms, as well as to applications, for example in fluid dynamics, electromagnetic fields, structural mechanics, free boundary problems. The book will be very useful for a wide range of readers, giving them an excellent overview of the most modern methods, techniques, algorithms and results in numerical mathematics, scientific computing and their applications.

These proceedings collect the major part of the lectures given at ENU­ MATH2003, the European Conference on Numerical Mathematics and Ad­ vanced Applications, held in Prague, Czech Republic, from 18 August to 22 August, 2003. The importance of numerical and computational mathematics and sci­ entific computing is permanently growing. There is an increasing number of different research areas, where numerical simulation is necessary. Let us men­ tion fluid dynamics, continuum mechanics, electromagnetism, phase transi­ tion, cosmology, medicine, economics, finance, etc. The success of applications of numerical methods is conditioned by changing its basic instruments and looking for new appropriate techniques adapted to new problems as well as new computer architectures. The ENUMATH conferences were established in order to provide a fo­ rum for discussion of current topics of numerical mathematics. They seek to convene leading experts and young scientists with special emphasis on con­ tributions from Europe. Recent results and new trends are discussed in the analysis of numerical algorithms as well as in their applications to challenging scientific and industrial problems. The first ENUMATH conference was organized in Paris in 1995, then the series continued by the conferences in Heidelberg 1997, Jyvaskyla 1999 and Ischia Porto 2001. It was a great pleasure and honour for the Czech numerical community that it was decided at Ischia Porto to organize the ENUMATH2003 in Prague. It was the first time when this conference crossed the former Iron Courtain and was organized in a postsocialist country.

As a satellite conference of the 1998 International Mathematical Congress and part of the celebration of the 650th anniversary of Charles University, the Partial Differential Equations Theory and Numerical Solution conference was held in Prague in August, 1998. With its rich scientific program, the conference provided an opportunity for almost 200 participants to gather and discuss emerging directions and recent developments in partial differential equations (PDEs).This volume comprises the Proceedings of that conference. In it, leading specialists in partial differential equations, calculus of variations, and numerical analysis present up-to-date results, applications, and advances in numerical methods in their fields. Conference organizers chose the contributors to bring together the scientists best able to present a complex view of problems, starting from the modeling, passing through the mathematical treatment, and ending with numerical realization. The applications discussed include fluid dynamics, semiconductor technology, image analysis, motion analysis, and optimal control.The importance and quantity of research carried out around the world in this field makes it imperative for researchers, applied mathematicians, physicists and engineers to keep up with the latest developments. With its panel of international contributors and survey of the recent ramifications of theory, applications, and numerical methods, Partial Differential Equations: Theory and Numerical Solution provides a convenient means to that end.

The book is the Proceedings of the Conference ENUMATH 2003, the 5th European Conference on Numerical Mathematics, concerned with most recent achievements in scientific computing, computational mathematics, numerical analysis and their applications. These proceedings contain a selection of invited plenary lectures, papers presented in minisymposia and contributed papers. All contributions to these proceedings have been reviewed by members of the Scientific Committee. Attention is paid to theoretical aspects of new numerical techniques and algorithms, as well as to applications, for example in fluid dynamics, electromagnetic fields, structural mechanics, free boundary problems. The book will be very useful for a wide range of readers, giving them an excellent overview of the most modern methods, techniques, algorithms and results in numerical mathematics, scientific computing and their applications.

These proceedings collect the major part of the lectures given at ENU­ MATH2003, the European Conference on Numerical Mathematics and Ad­ vanced Applications, held in Prague, Czech Republic, from 18 August to 22 August, 2003. The importance of numerical and computational mathematics and sci­ entific computing is permanently growing. There is an increasing number of different research areas, where numerical simulation is necessary. Let us men­ tion fluid dynamics, continuum mechanics, electromagnetism, phase transi­ tion, cosmology, medicine, economics, finance, etc. The success of applications of numerical methods is conditioned by changing its basic instruments and looking for new appropriate techniques adapted to new problems as well as new computer architectures. The ENUMATH conferences were established in order to provide a fo­ rum for discussion of current topics of numerical mathematics. They seek to convene leading experts and young scientists with special emphasis on con­ tributions from Europe. Recent results and new trends are discussed in the analysis of numerical algorithms as well as in their applications to challenging scientific and industrial problems. The first ENUMATH conference was organized in Paris in 1995, then the series continued by the conferences in Heidelberg 1997, Jyvaskyla 1999 and Ischia Porto 2001. It was a great pleasure and honour for the Czech numerical community that it was decided at Ischia Porto to organize the ENUMATH2003 in Prague. It was the first time when this conference crossed the former Iron Courtain and was organized in a postsocialist country.