Galerkin Finite Element Methods for Parabolic Problems
Edition: 2nd edition
Publisher: Springer
Published: August 21, 2006
Language: eng
Format: Hardcover
Number of pages: 370
ISBN-13: 9783540331216
Subjects: Differential equations; Mathematical theory of computation; Number theory; Number Systems; Mathematics; Science/Mathematics; Mathematical Analysis; Mathematical Physics; Galerkin methods; Mathematics / Number Systems; finite element theory; parabolic partial
Description: 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.
Notes: Springer Series in Computational Mathematics