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Titlebook: Numerical Analysis; Roger Temam Book 1973 D. Reidel Publishing Company, Dordrecht, Holland 1973 Approximation.calculus.finite element meth

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發(fā)表于 2025-3-21 17:27:14 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書(shū)目名稱(chēng)Numerical Analysis
編輯Roger Temam
視頻videohttp://file.papertrans.cn/669/668913/668913.mp4
圖書(shū)封面Titlebook: Numerical Analysis;  Roger Temam Book 1973 D. Reidel Publishing Company, Dordrecht, Holland 1973 Approximation.calculus.finite element meth
描述This book is an introduction to one of the important as- pects of Numerical Analysis, namely the approximate solution of functional equations. We intend to show, by a few brief examples, the different theoretical and practical problems related to the numerical approximation of boundary value problems. We have chosen for this the approximate solution of certain linear elliptic partial differential equations (the first two parts of the book) and the approximate solution of a nonlinear elliptic differential equation. This book is not a systematic study of the subject, but the methods developed here can be applied to large classes of linear and nonlinear elliptic problems. The book assumes that the reader‘s knowledge of Anal- ysis is comparable to what is taught in the first years of graduate studies. This means a good knowledge of Hilbert spaces, elements of measure theory and theory of distributions. The subject matter of the book covers the usual content of a first course on Numerical Analysis of partial differential equations.
出版日期Book 1973
關(guān)鍵詞Approximation; calculus; finite element method; numerical analysis
版次1
doihttps://doi.org/10.1007/978-94-010-2565-2
isbn_softcover978-94-010-2567-6
isbn_ebook978-94-010-2565-2
copyrightD. Reidel Publishing Company, Dordrecht, Holland 1973
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comparable to what is taught in the first years of graduate studies. This means a good knowledge of Hilbert spaces, elements of measure theory and theory of distributions. The subject matter of the book covers the usual content of a first course on Numerical Analysis of partial differential equations.978-94-010-2567-6978-94-010-2565-2
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Approximation of Some Function Spaces by Finite Element Methodsstep functions, but functions defined on a set of .-simplices contained in Ω Inside the simplex the approximating function is a simple function, a linear function in the simplest case, or some type of polynomial function of restricted degree in more refined situations. We will only consider approxim
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The Projection TheoremIn this chapter we prove a very simple theorem, known as the projection theorem or Lax-Milgram theorem. It implies existence and uniqueness of ‘weak’ solutions for certain classes of linear elliptic problems. In Part II, two applications are developed (cf. Chapter 7; Sections 11.1 and 12.1).
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發(fā)表于 2025-3-22 19:19:58 | 只看該作者
The Method of GalerkinThe aim of the following chapters is to study the approximation of the solution of problem (1.2). To begin with, we present here the method of Galerkin and we will see how this leads to an approximate solution of Equation (1.2).
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發(fā)表于 2025-3-22 22:15:19 | 只看該作者
Approximation of Linear Variational ProblemsWe study here the approximate solution of Equation (1.2) in a general setting, that covers the method of Galerkin, which we have already seen, as well as the finite difference and finite element methods. Examples are worked out in Sections 11.2, 11.3 and 12.2.
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發(fā)表于 2025-3-23 09:13:12 | 只看該作者
The Method of Fractionary StepsWe are now going to study a new method of solving Equation (1.2). In fact, the following can also be applied to the solution of the discretized Equation (4.3).
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