Robust numerical methods for singularly perturbed differential equations : convection-diffusion-reaction and flow problems Hans-Görg Roos; M Stynes; L Tobiska

By:

Roos, Hans-Görg

Contributor(s):

Material type: Text

9783540344667

Subject(s):

DDC classification:

518.63 ROO

Contents:

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.

Summary: 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.

List(s) this item appears in: New Arrivals April - June 2022

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Holdings
Item type	Current library	Collection	Call number	Status	Date due	Barcode
Books	IIITDM Kurnool General Stacks	Non-fiction	518.63 ROO (Browse shelf(Opens below))	Checked out	26.08.2025	0004593

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.

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.

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