TY - BOOK AU - Roos, Hans-Görg AU - Stynes, M. AU - Tobiska, L. TI - Robust numerical methods for singularly perturbed differential equations : : convection-diffusion-reaction and flow problems SN - 9783540344667 U1 - 518.63 PY - 2008/// CY - Berlin : PB - Springer-Verlag KW - Singular perturbations (Mathematics) KW - Numerical analysis KW - Navier-Stokes equations KW - Boundary value problems KW - Finite element method KW - Differential equations--Numerical solutions KW - Mathematics KW - Statistics N1 - pt. 1. Ordinary differential equations. -- ; The analytical behaviour of solutions -- ; Numerical methods for second-order boundary value problems --; pt. 2. Parabolic initial-boundary value problems in one space dimension. -- ; Introduction -- ; Analytical behaviour of solutions -- ; Finite difference methods -- ; Finite element methods -- ; Two adaptive methods --; pt. 3. Elliptic and parabolic problems in several space dimensions. -- ; Analytical behaviour of solutions -- ; Finite difference methods -- ; Finite element methods -- ; Time-dependent problems --; pt. 4. The incompressible Navier-Stokes equations. -- ; Existence and uniqueness results -- ; Upwind finite element method -- ; Higher-order methods of streamline diffusion type -- ; Local projection stabilization for equal-order interpolation -- ; Local projection method for Inf-Sup stable elements -- ; Mass conservation for coupled flow-transport problems -- ; Adaptive error control N2 - This considerably expanded and completely revised second edition incorporates many new developments in the thriving field of numerical methods for singularly perturbed differential equations. It provides a thorough foundation for the numerical analysis and solution of these problems, which model many physical phenomena whose solutions exhibit layers. The book focuses on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics. It offers a comprehensive overview of suitable numerical methods while emphasizing those with realistic error estimates. The book should be useful for scientists requiring effective numerical methods for singularly perturbed differential equations ER -