Bücher der Reihe Springer Series in Computational Mathematics

This book is devoted to the mathematical analysis of the numerical solution of boundary integral equations treating boundary value, transmission and contact problems arising in elasticity, acoustic and electromagnetic scattering. It serves as the mathematical foundation of the boundary element methods (BEM) both for static and dynamic problems. The book presents a systematic approach to the variational methods for boundary integral equations including the treatment with variational inequalities for contact problems. It also features adaptive BEM, hp-version BEM, coupling of finite and boundary element methods - efficient computational tools that have become extremely popular in applications.Familiarizing readers with tools like Mellin transformation and pseudodifferential operators as well as convex and nonsmooth analysis for variational inequalities, it concisely presents efficient, state-of-the-art boundary element approximations and points to up-to-date research.The authors are well known for their fundamental work on boundary elements and related topics, and this book is a major contribution to the modern theory of the BEM (especially for error controlled adaptive methods and for unilateral contact and dynamic problems) and is a valuable resource for applied mathematicians, engineers, scientists and graduate students.

Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed presentation of basic spectral algorithms, as well as a systematical presentation of basic convergence theory and error analysis for spectral methods.

This book deals with methods for solving nonstiff ordinary differential equations. The reader will benefit from many illustrations, a historical and didactic approach, and computer programs. This new edition has been rewritten and new material has been included.

This book covers numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions.

This book covers the solution of stiff differential equations and of differential-algebraic systems. This second edition contains new material including numerical tests, recent progress in numerical differential-algebraic equations, and improved FORTRAN codes.

Here is a framework for mixed finite element methods, moving from a finite dimensional presentation, then on to formulation in Hilbert spaces and approximations, stabilized methods and eigenvalue problems. Offers examples: Stokes' problem, elasticity and more.

However, the technique of hierarchical matrices makes it possible to store matrices and to perform matrix operations approximately with almost linear cost and a controllable degree of approximation error.

This book explores finite element methods for incompressible flow problems: Stokes equations, stationary Navier-Stokes equations and time-dependent Navier-Stokes equations. The proofs are presented step by step, allowing readers to more easily understand the analytical techniques.

This book introduces the concepts and methodologies related to the modelling of complex phenomena occurring in materials processing, developing finite differences, finite volumes and finite elements through phase transformation, solid mechanics and fluid flow.

This new edition incorporates new developments in numerical methods for singularly perturbed differential equations, focusing on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics.

This work presents a thorough treatment of boundary element methods (BEM) for solving strongly elliptic boundary integral equations obtained from boundary reduction of elliptic boundary value problems in $\mathbb{R}^3$.

As suggested by the title of this book Numerical Toolbox for Verified Computing, we present an extensive set of sophisticated tools to solve basic numerical problems with a verification of the results.

The subject of the book is the mathematical theory of the discontinuous Galerkin method (DGM), which is a relatively new technique for the numerical solution of partial differential equations.

"Contains numerous simple examples and illustrative diagrams....For anyone seeking information about eigenvalue inclusion theorems, this book will be a great reference." Gersgorin who wrote a seminal paper in 1931 on how to easily obtain estimates of all n eigenvalues (characteristic values) of any given n-by-n complex matrix.

The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations.

This book provides an up-to-date introduction to the time-domain finite element methods for Maxwell's equations involving metamaterials, focusing on practical implementation of edge finite element methods for metamaterial Maxwell's equations.

This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite and in infinite dimension. Its focus is on local and global Newton methods for direct problems or Gauss-Newton methods for inverse problems.

Multi-grid methods are the most efficient tools for solving elliptic boundary value problems. One section describes special applications (convection-diffusion equations, singular perturbation problems, eigenvalue problems, etc.).

This is the soft cover reprint of the very popular hardcover edition. The book offers a simultaneous presentation of the theory and of the numerical treatment of elliptic problems.

Unique book on Reaction-Advection-Diffusion problems

This monograph is the first to provide readers with numerical tools for a systematic analysis of bifurcation problems in reaction-diffusion equations. Readers will gain a thorough understanding of numerical bifurcation analysis and the necessary tools for investigating nonlinear phenomena in reaction-diffusion equations.

This book provides insight into the mathematics of Galerkin finite element method as applied to parabolic equations. Two new chapters have also been added, dealing with problems in polygonal, particularly noncovex, spatial domains, and with time discretization based on using Laplace transformation and quadrature.

LANCELOT is a software package for solving large-scale nonlinear optimization problems. Although the book is primarily concerned with a specific optimization package, the issues discussed have much wider implications for the design and im plementation of large-scale optimization algorithms.

Stochastic numerical methods play an important role in large scale computations in the applied sciences. The first goal of this book is to give a mathematical description of classical direct simulation Monte Carlo (DSMC) procedures for rarefied gases, using the theory of Markov processes as a unifying framework.

This book examines numerical methods for two-phase incompressible flow problems. It details the complete simulation track, from modeling via development and analysis of numerical methods to numerical experiments.