This volume will contain selected papers from the lectures held at the BAIL 2010 Conference, which took place from July 5th to 9th, 2010 in Zaragoza (Spain). The papers present significant advances in the modeling, analysis and construction of efficient numerical methods to solve boundary and interior layers appearing in singular perturbation problems. Special emphasis is put on the mathematical foundations of such methods and their application to physical models. Topics in scientific fields such as fluid dynamics, quantum mechanics, semiconductor modeling, control theory, elasticity, chemical reactor theory, and porous media are examined in detail.

This volume will contain selected papers from the lectures held at the BAIL 2010 Conference, which took place from July 5th to 9th, 2010 in Zaragoza (Spain). The papers present significant advances in the modeling, analysis and construction of efficient numerical methods to solve boundary and interior layers appearing in singular perturbation problems. Special emphasis is put on the mathematical foundations of such methods and their application to physical models. Topics in scientific fields such as fluid dynamics, quantum mechanics, semiconductor modeling, control theory, elasticity, chemical reactor theory, and porous media are examined in detail.

This book deals with the efficient solution of the large sparse systems of equations arising from the discretization of partial differential equations (PDEs) which mathematically model problems encountered in many applications to physics and engineering. This issue is one of the most important aspects in the numerical solution of many problems, and therefore it deserves important attention. With this purpose, our primary interest here is to design efficient finite element geometric multigrid methods on semi-structured triangular grids. To this end, a local Fourier analysis (LFA) on triangular grids is presented in this book, resulting in a very useful tool to choose suitable components of multigrid methods. The practical utility of this approach is illustrated with some examples of scalar and vector problems.