This book provides insight into the mathematics of Galerkin finite element method as applied to parabolic equations. The revised second edition has been influenced by recent progress in application of semigroup theory to stability and error analysis, particulatly in maximum-norm. Two new chapters have also been added, dealing with problems in polygonal, particularly noncovex, spatial domains, and with time discretization based on using Laplace transformation and quadrature.
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This book provides insight in the mathematics of Galerkin finite element method as applied to parabolic equations. The approach is based on first discretizing in the spatial variables by Galerkin's method, using piecewise polynomial trial functions, and then applying some single step or multistep time stepping method. The concern is stability and error analysis of approximate solutions in various norms, and under various regularity assumptions on the exact solution. The book gives an excellent insight in the present ideas and methods of analysis. The second edition has been influenced by recent progress in application of semigroup theory to stability and error analysis, particulatly in maximum-norm. Two new chapters have also been added, dealing with problems in polygonal, particularly noncovex, spatial domains, and with time discretization based on using Laplace transformation and quadrature.
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1 of 1 people found the following review helpful:
5.0 out of 5 stars
a solid book,
By A Customer
This review is from: Galerkin Finite Element Methods for Parabolic Problems (Springer Series in Computational Mathematics) (Hardcover)
this book presents a very deep and solid review of the theory of finite elements for parabolic problems. is the ideal book to dictate a graduate course on the field, as well as for learning from it as an specialist. it has a very extensive and up-to-date references list.the reading of this book needs the knowledge of some basic theory on finite elements approximation, and a little bit of PDE's theory. However, this knowledge is not indispensable. summarizing, it is an exelent book. rigorous but also very pedagogical, and not very difficult to read.
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Key Phrases - Statistically Improbable Phrases (SIPs):
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spatially semidiscrete problem, quasiuniform family, nonsmooth data error estimate, homogeneous parabolic equation, semidiscrete analogue, discrete initial data, semidiscrete solution, nonsmooth initial data, quasiuniform triangulations, semidiscrete equation, nonconvex corner, elliptic regularity estimate, lumped mass method, negative norm estimates, data error estimates, appropriate regularity assumptions, elliptic projection, homogeneous heat equation, optimal order error estimates, resolvent estimate, time discretization scheme, inverse estimate, parabolic problem, backward difference method, following error estimate Key Phrases - Capitalized Phrases (CAPs): (learn more)
Euler Galerkin, Crank-Nicolson Galerkin, Using the Cauchy-Schwarz New!
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spatially semidiscrete problem, quasiuniform family, nonsmooth data error estimate, homogeneous parabolic equation, semidiscrete analogue, discrete initial data, semidiscrete solution, nonsmooth initial data, quasiuniform triangulations, semidiscrete equation, nonconvex corner, elliptic regularity estimate, lumped mass method, negative norm estimates, data error estimates, appropriate regularity assumptions, elliptic projection, homogeneous heat equation, optimal order error estimates, resolvent estimate, time discretization scheme, inverse estimate, parabolic problem, backward difference method, following error estimate Key Phrases - Capitalized Phrases (CAPs): (learn more)
Euler Galerkin, Crank-Nicolson Galerkin, Using the Cauchy-Schwarz 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)
11
books
cite this book:
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- Scientific Computing in Electrical Engineering by Ursula van Rienen on page 386
- Comparison Methods and Stability Theory (Lecture Notes in Pure and Applied Mathematics) by Liu on page 268
- Numerical Analysis and Its Applications: Third International Conference, NAA 2004, Rousse, Bulgaria, June 29 - July 3, 2004, Revised Selected Papers ... Computer Science and General Issues) by Zhilin Li on page 6
- Trends in Nonlinear Analysis by Markus Kirkilionis on page 321
- Finite Element Methods for Integrodifferential Equations (Series on Applied Mathematics) by Chuanmiao Chen in Back Matter
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