Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in reยญ search and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numeriยญ cal and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. T AM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Matheยญ matical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs
CONTENT
0 Basic Concepts -- 1 Sobolev Spaces -- 2 Variational Formulation of Elliptic Boundary Value Problems -- 3 The Construction of a Finite Element Space -- 4 Polynomial Approximation Theory in Sobolev Spaces -- 5 n-Dimensional Variational Problems -- 6 Finite Element Multigrid Methods -- 7 Additive Schwarz Preconditioners -- 8 Maxโ{128}{148}norm Estimates -- 9 Adaptive Meshes -- 10 Variational Crimes -- 11 Applications to Planar Elasticity -- 12 Mixed Methods -- 13 Iterative Techniques for Mixed Methods -- 14 Applications of Operator-Interpolation Theory -- References
