Discontinuous Galerkin (DG) methods for solving partial differential equations, developed in the late 1990s, have become popular among computational scientists. This book covers both theory and computation as it focuses on three primal DG methods - the symmetric interior penalty Galerkin, incomplete interior penalty Galerkin, and nonsymmetric ......
Methods for the numerical simulation of dynamic mathematical models have been the focus of intensive research for well over 60 years, and the demand for better and more efficient methods has grown as the range of applications has increased. Mathematical models involving evolutionary partial differential equations (PDEs) as well as ordinary ......
Addresses the increasingly-important role of numerical methods in science and engineering. While treating traditional and well-developed topics, it also emphasizes concepts and ideas of importance to the design of accurate and efficient algorithms with applications to scientific computing. Although this volume is self-contained, more comprehensive ......
Numerical Solutions of PDEs Involving Interfaces and Irregular Domains
Interface problems arise when there are two different materials, such as water and oil, or the same material at different states, such as water and ice. If partial or ordinary differential equations are used to model these applications, the parameters in the governing equations are typically discontinuous across the interface separating the two ......
The Lanczos Method: Evolution and Application is divided into two distinct parts. The first part reviews the evolution of one of the most widely used numerical techniques in the industry. The development of the method, as it became more robust, is demonstrated through easy-to-understand algorithms. The second part contains industrial applications ......
When M. Vidyasagar wrote the first edition of Nonlinear Systems Analysis, most control theorists considered the subject of nonlinear systems a mystery. Since then, advances in the application of differential geometric methods to nonlinear analysis have matured to a stage where every control theorist needs to possess knowledge of the basic ......
First published in 1985, this book presents background material, descriptions, and supporting theory relating to practical numerical algorithms for the solution of huge elgenvalue problems. It deals with "symmetric" problems. However, in this book, "symmetric" also encompasses numerical procedures for computing singular values and vectors of real ......
Accuracy and Stability of Numerical Algorithms gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. This second edition expands and ......
This text provides an in-depth analysis of the mathematical foundations of the finite element method. It is a comprehensive reference and introduction to current research on the numerical analysis of the finite element method, as well as a working textbook for graduate courses in numerical analysis. It includes many useful figures and exercises of ......
