My purpose in this monograph is to present an essentially self-contained account of the mathematical theory of Galerkin ?nite element methods as appliedtoparabolicpartialdi?erentialequations. Theemphasesandselection of topics re?ects my own involvement in the ?eld over the past 25 years, and my ambition has been to stress ideas and methods of analysis rather than to describe the most general and farreaching results possible. Since the formulation and analysis of Galerkin ?nite element methods for parabolic problems are generally based on ideas and results from the corresponding theory for...
My purpose in this monograph is to present an essentially self-contained account of the mathematical theory of Galerkin ?nite element methods as appli...
The Eighth EPSRC Numerical Analysis Summer School was held at the Uni- versity of Leicester from the 5th to the 17th of July, 1998. This was the third Numerical Analysis Summer School to be held in Leicester. The previous meetings, in 1992 and 1994, had been carefully structured to ensure that each week had a coherent 'theme'. For the 1998 meeting, in order to widen the audience, we decided to relax this constraint. Speakers were chosen to cover what may appear, at first sight, to be quite diverse areas of numeri- cal analysis. However, we were pleased with the extent to which the ideas...
The Eighth EPSRC Numerical Analysis Summer School was held at the Uni- versity of Leicester from the 5th to the 17th of July, 1998. This was the third...
Many books have been written on ?nite difference methods (FDM), but there are good reasons to write still another one. The main reason is that even if higher order methods have been known for a long time, the analysis of stability, accuracy and effectiveness is missing to a large extent. For example, the de?nition of the formal high order accuracy is based on the assumption that the true solution is smooth, or expressed differently, that the grid is ?ne enough such that all variations in the solution are well resolved. In many applications, this assumption is not ful?lled, and then it is...
Many books have been written on ?nite difference methods (FDM), but there are good reasons to write still another one. The main reason is that even if...
TheGer? sgorin CircleTheorem, averywell-known resultin linear algebra today, stems from the paper of S. Ger? sgorin in 1931 (which is reproduced in AppendixD)where, givenanarbitrarynncomplexmatrix, easyarithmetic operationsontheentriesofthematrixproducendisks, inthecomplexplane, whose union contains all eigenvalues of the given matrix. The beauty and simplicity of Ger? sgorin's Theorem has undoubtedly inspired further research in this area, resulting in hundreds of papers in which the name "Ger? sgorin" appears. The goal of this book is to give a careful and up-to-date treatment of various...
TheGer? sgorin CircleTheorem, averywell-known resultin linear algebra today, stems from the paper of S. Ger? sgorin in 1931 (which is reproduced in Ap...
Special numerical techniques are already needed to deal with nxn matrices for large n.Tensor data are of size nxnx...xn=n DEGREESd, where n DEGREESd exceeds the computer memory by far. They appear for problems of high spatial dimensions. Since standard methods fail, a particular tensor calculus is needed to treat such problems. The monograph describes the methods how tensors can be practically treated and how numerical operations can be performed. Applications are problems from quantum chemistry, approximation of multivariate functions, solution of pde, e.g., with stochastic coefficients
Special numerical techniques are already needed to deal with nxn matrices for large n.Tensor data are of size nxnx...xn=n DEGREESd, where n DEGREESd e...
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.
This book examines numerical methods for two-phase incompressible flow problems. It details the complete simulation track, from modeling via developme...
Many mathematicians, scientists, and engineers are familiar with the Fast Fourier Transform, a method based upon the Discrete Fourier Transform. Perhaps not so many mathematicians, scientists, and engineers recognize that the Discrete Fourier Transform is one of a family of symbolic formulae called Sinc methods. Sinc methods are based upon the Sinc function, a wavelet-like function replete with identities which yield approximations to all classes of computational problems. Such problems include problems over finite, semi-infinite, or infinite domains, problems with singularities, and boundary...
Many mathematicians, scientists, and engineers are familiar with the Fast Fourier Transform, a method based upon the Discrete Fourier Transform. Perha...
Designed to give a contemporary international survey of research activities in approximation theory and special functions, this book brings together the work of approximation theorists from North America, Western Europe, Asia, Russia, the Ukraine, and several other former Soviet countries. Contents include: results dealing with q-hypergeometric functions, differencehypergeometric functions and basic hypergeometric series with Schur function argument; the theory of orthogonal polynomials and expansions, including generalizations of Szego type asymptotics and connections with Jacobi matrices;...
Designed to give a contemporary international survey of research activities in approximation theory and special functions, this book brings together t...
Research on non-standard finite element methods is evolving rapidly and in this text Brezzi and Fortin give a general framework in which the development is taking place. The presentation is built around a few classic examples: Dirichlet's problem, Stokes problem, Linear elasticity. The authors provide with this publication an analysis of the methods in order to understand their properties as thoroughly as possible.
Research on non-standard finite element methods is evolving rapidly and in this text Brezzi and Fortin give a general framework in which the developme...
The subject of this book is the introduction and application of a new measure for smoothness offunctions. Though we have both previously published some articles in this direction, the results given here are new. Much of the work was done in the summer of 1984 in Edmonton when we consolidated earlier ideas and worked out most of the details of the text. It took another year and a half to improve and polish many of the theorems. We express our gratitude to Paul Nevai and Richard Varga for their encouragement. We thank NSERC of Canada for its valuable support. We also thank Christine Fischer and...
The subject of this book is the introduction and application of a new measure for smoothness offunctions. Though we have both previously published som...