Since their emergence, finite element methods have taken a place as one of the most versatile and powerful methodologies for the approximate numerical solution of Partial Differential Equations. These methods are used in incompressible fluid flow, heat, transfer, and other problems. This book provides researchers and practitioners with a concise guide to the theory and practice of least-square finite element methods, their strengths and weaknesses, established successes, and open problems.

This is the first monograph on the subject, providing a comprehensive introduction to the LSFEM method for numerical solution of PDEs. LSFEM is simple, efficient and robust, and can solve a wide range of problems in fluid dynamics and electromagnetics.

Since their emergence, finite element methods have taken a place as one of the most versatile and powerful methodologies for the approximate numerical solution of Partial Differential Equations. These methods are used in incompressible fluid flow, heat, transfer, and other problems. This book provides researchers and practitioners with a concise guide to the theory and practice of least-square finite element methods, their strengths and weaknesses, established successes, and open problems.

Advances in Applied Mechanics

This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.​

ICSSD 2002 is the second in the series of International Conferences on Structural Stability and Dynamics, which provides a forum for the exchange of ideas and experiences in structural stability and dynamics among academics, engineers, scientists and applied mathematicians. Held in the modern and vibrant city of Singapore, ICSSD 2002 provides a peep at the areas which experts on structural stability and dynamics will be occupied with in the near future. From the technical sessions, it is evident that well-known structural stability and dynamic theories and the computational tools have evolved to an even more advanced stage. Many delegates from diverse lands have contributed to the ICSSD 2002 proceedings, along with the participation of colleagues from the First Asian Workshop on Meshfree Methods and the International Workshop on Recent Advances in Experiments and Computations on Modeling of Heterogeneous Systems. Forming a valuable source for future reference, the proceedings contain 153 papers OCo including 3 keynote papers and 23 invited papers OCo contributed by authors from all over the world who are working in advanced multi-disciplinary areas of research in engineering. All these papers are peer-reviewed, with excellent quality, and cover the topics of structural stability, structural dynamics, computational methods, wave propagation, nonlinear analysis, failure analysis, inverse problems, non-destructive evaluation, smart materials and structures, vibration control and seismic responses.The major features of the book are summarized as follows: a total of 153 papers are included with many of them presenting fresh ideas and new areas of research; all papers have been peer-reviewed and are grouped into sections for easy reference; wide coverage of research areas is provided and yet there is good linkage with the central topic of structural stability and dynamics; the methods discussed include those that are theoretical, analytical, computational, artificial, evolutional and experimental; the applications range from civil to mechanical to geo-mechanical engineering, and even to bioengineering."