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 research 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 numerical 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 encourage the teaching of new courses. tam will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the applied math- ematical sciences (ams) series, which will focus on advanced textbooks and research level monographs.
本书文英文版。
目录
Preface 0 Basic Concepts 0.1 Weak Formulation of Boundary Value Problems 0.2 Ritz-Galerkin Approximation 0.3 Error Estimates 0.4 Piecewise Polynomial Spaces - The Finite Element Method 0.5 Relationship to Difference Methods 0.6 Computer Implementation of Finite Element Methods 0.7 Local Estimates 0.8 Weighted Norm Estimates 0.x Exercises 1 Sobolev Spaces 1.1 Review of Lebesgue Integration Theory 1.2 Generalized (weak) Derivatives 1.3 Sobolev Norms and Associated Spaces 1.4 Inclusion Relations and Sobolev‘s Inequality 1.5 Review of Chapter 0 1.6 Trace Theorems 1.7 Negative Norms and Duality 1.x Exercises 2 Variationla Formulation of Elliptic Boundary Value Problems 2.1 Inner-Product Spaces 2.2 Hilbert Spaces 2.3 Projections onto Subspaces …… 3 The Construction of a Finite Element Space 4 Polynomial Approximtion Theory in Sobolev Spaces 5 n-Dimensional Variational Problems 6 Finite Element Multigrid Methods 7 Max-norm Estimates 8 Variational Crimes 9 Applications to Planar Elasticity 10 Mixed Methods 11 Iterative Techniques for Mixed Methods 12 Applications of Operator-Interpolation Theory References Index
