In accordance with the developments in computation, theoretical studies on numerical schemes are now fruitful and highly needed. In 1991 an article on the finite element method applied to evolutionary problems was published. Following the method, basically this book studies various schemes from operator theoretical points of view. Many parts are devoted to the finite element method, but other schemes and problems (charge simulation method, domain decomposition method, nonlinear problems, and so forth) are also discussed, motivated by the observation that practically useful schemes have fine mathematical structures and the converses are also true. This book has the following chapters: 1. Boundary Value Problems and FEM. 2. Semigroup Theory and FEM. 3. Evolution Equations and FEM. 4. Other Methods in Time Discretization. 5. Other Methods in Space Discretization. 6. Nonlinear Problems. 7. Domain Decomposition Method.
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Editorial Reviews
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Calin Ioan Gheorghiu
The authors provide a very sharp theoretical study of numerical methods used to solve partial diferential equations of elliptic and parabolic type. Every numerical scheme is thoroughly dissected. As a whole, everything fits together in a harmonious way.
Zentrallblatt fur Mathematik
Charles W. Groetsch
The book is efficiently organized and each chapter concludes with a very informative commentary section that provides brief but useful historical, bibliographical or technical comments.
Mathematical Reviews
The authors provide a very sharp theoretical study of numerical methods used to solve partial diferential equations of elliptic and parabolic type. Every numerical scheme is thoroughly dissected. As a whole, everything fits together in a harmonious way.
Zentrallblatt fur Mathematik
Charles W. Groetsch
The book is efficiently organized and each chapter concludes with a very informative commentary section that provides brief but useful historical, bibliographical or technical comments.
Mathematical Reviews
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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degenerate parabolic equations, space discretization, asymptotic expansion, mixed finite elements, charge simulation method, hyperbolic equation, boundary element method, inverse assumption, semidiscrete finite element approximation, amplification operator, elliptic estimate, semidiscrete approximation, holomorphic semigroup, discrete maximum principle, elliptic boundary value problems, semilinear parabolic equations, variational structure, semigroup theory, harmonic extension, adjoint form, unique solvability, domain decomposition method, duality argument Key Phrases - Capitalized Phrases (CAPs): (learn more)
Other Methods, Proof of Theorem, Nonlinear Problems, Multi-step Method, The Stokes System, Alternative Approach, Lumping of Mass, Generation Theories, Neumann Iteration New!
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Front Cover | Table of Contents | First Pages | Index | Surprise Me!
degenerate parabolic equations, space discretization, asymptotic expansion, mixed finite elements, charge simulation method, hyperbolic equation, boundary element method, inverse assumption, semidiscrete finite element approximation, amplification operator, elliptic estimate, semidiscrete approximation, holomorphic semigroup, discrete maximum principle, elliptic boundary value problems, semilinear parabolic equations, variational structure, semigroup theory, harmonic extension, adjoint form, unique solvability, domain decomposition method, duality argument Key Phrases - Capitalized Phrases (CAPs): (learn more)
Other Methods, Proof of Theorem, Nonlinear Problems, Multi-step Method, The Stokes System, Alternative Approach, Lumping of Mass, Generation Theories, Neumann Iteration New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
Citations (learn more)
This book cites 25
books:
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1
book
cites this book:
- Domain Decomposition Methods by Andrea Toselli on 5 pages
- Numerical Analysis (Proceedings of Symposia in Applied Mathematics, V. 22) by American Mathematical Society in Back Matter (1), and Back Matter (2)
- Partial Differential Equations (Applied Mathematical Sciences) (v. 1) by Fritz John in Back Matter (1), and Back Matter (2)
- Elliptic Partial Differential Equations of Second Order by David Gilbarg in Back Matter
- Numerical Solution of Partial Differential Equations by the Finite Element Method by Claes Johnson in Back Matter
See all 25 books this book cites
- Applied analysis: mathematical methods in natural science by Takasi Senba in Back Matter
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