This book deals with the numerical approximation of partial differential equations. Its scope is to provide a thorough illustration of numerical methods, carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is one of its main features. Many kinds of problems are addressed. A comprehensive theory of Galerkin method and its variants, as well as that of collocation methods, are developed for the spatial discretization. These theories are then specified to two numerical subspace realizations of remarkable interest: the finite element method and the spectral method.
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"...The book is excellent and is addressed to post-graduate students, research workers in applied sciences as well as to specialists in numerical mathematics solving PDE. Since it is written very clearly, it would be acceptable for undergraduate students in advanced courses of numerical mathematics. Readers will find this book to be a great pleasure."--MATHEMATICAL REVIEWS
--This text refers to an alternate Hardcover edition.From the Back Cover
This book deals with the numerical approximation of partial differential equations. Its scope is to provide a thorough illustration of numerical methods, carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is one of its main features. Many kinds of problems are addressed. A comprehensive theory of Galerkin method and its variants, as well as that of collocation methods, are developed for the spatial discretization. These theories are then specified to two numerical subspace realizations of remarkable interest: the finite element method and the spectral method. From the reviews: "...The book is excellent and is addressed to post-graduate students, research workers in applied sciences as well as to specialists in numerical mathematics solving PDE. Since it is written very clearly, it would be acceptable for undergraduate students in advanced courses of numerical mathematics. Readers will find this book to be a great pleasure."--MATHEMATICAL REVIEWS
--This text refers to the
Paperback
edition.
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First Sentence:
Numerical approximation of partial differential equations is an important branch of Numerical Analysis. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
spectral collocation approximation, spectral collocation method, natural matrix norm, collocation case, collocation problem, discrete scalar product, finite element case, numerical flux function, spectral condition number, positive definite with respect, coerciveness assumption, spurious pressure modes, domain decomposition methods, second order elliptic problems, collocation nodes, collocation solution, bubble functions, optimal error estimates, following error estimate, interelement boundaries, finite element stiffness, spectral approximations, inverse inequality, stabilizing term, mixed finite element methods Key Phrases - Capitalized Phrases (CAPs): (learn more)
Legendre Gauss-Lobatto, Chebyshev Gauss-Lobatto, Legendre Expansion New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Numerical approximation of partial differential equations is an important branch of Numerical Analysis. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
spectral collocation approximation, spectral collocation method, natural matrix norm, collocation case, collocation problem, discrete scalar product, finite element case, numerical flux function, spectral condition number, positive definite with respect, coerciveness assumption, spurious pressure modes, domain decomposition methods, second order elliptic problems, collocation nodes, collocation solution, bubble functions, optimal error estimates, following error estimate, interelement boundaries, finite element stiffness, spectral approximations, inverse inequality, stabilizing term, mixed finite element methods Key Phrases - Capitalized Phrases (CAPs): (learn more)
Legendre Gauss-Lobatto, Chebyshev Gauss-Lobatto, Legendre Expansion New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 97
books:
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54
books
cite this book:
See all 54 books citing this book
- Domain Decomposition Methods by Andrea Toselli on 22 pages
- Partial Differential Equations (Applied Mathematical Sciences) (v. 1) by Fritz John on 9 pages
- Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations (SIAM Proceedings in Applied Mathematics) by David E. Keyes on 5 pages
- Third International Symposium on Domain Decomposition Methods for Partial Differential Equations (Proceedings in Applied Mathematics) by International Symposium on Domain Decomposition Methods for Partial di on 5 pages
- Domain Decomposition Methods in Science and Engineering (Lecture Notes in Computational Science and Engineering) by Ralf Kornhuber on 4 pages
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- Applied and Industrial Mathematics in Italy: Proceedings of the 7th Conference (Series on Advances in Mathematics for Applied Sciences) by Mario Primicerio on page 64, and page 450
- Navier-Stokes Equations: Theory and Numerical Methods (Chapman & Hall/CRC Research Notes in Mathematics Series) by Rodolfo Salvi on page 288, and page 334
- Domain Decomposition Methods in Science and Engineering (Lecture Notes in Computational Science and Engineering) by Ralf Kornhuber on page 676
- Numerische Mathematik 2: Eine Einführung - unter Berücksichtigung von Vorlesungen von F.L.Bauer (Springer-Lehrbuch) (v. 2) (German Edition) by Josef Stoer on page 267
- Numerical Methods for Engineering Applications, 2nd Edition by Joel H. Ferziger in Back Matter
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