Galerkin Finite Element Methods for Parabolic Problems

• Κύριος συγγραφέας: Thomée, Vidar (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Σειρά: Springer Series in Computational Mathematics, 25
• Θέματα: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Numerical analysis.; Physics.; Numerical Analysis.; Analysis.; Theoretical, Mathematical and Computational Physics.

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 multist...

Πίνακας περιεχομένων:

• The Standard Galerkin Method
• Methods Based on More General Approximations of the Elliptic Problem
• Nonsmooth Data Error Estimates
• More General Parabolic Equations
• Negative Norm Estimates and Superconvergence
• Maximum-Norm Estimates and Analytic Semigroups
• Single Step Fully Discrete Schemes for the Homogeneous Equation
• Single Step Fully Discrete Schemes for the Inhomogeneous Equation
• Single Step Methods and Rational Approximations of Semigroups
• Multistep Backward Difference Methods
• Incomplete Iterative Solution of the Algebraic Systems at the Time Levels
• The Discontinuous Galerkin Time Stepping Method
• A Nonlinear Problem
• Semilinear Parabolic Equations
• The Method of Lumped Masses
• The H1 and H?1 Methods
• A Mixed Method
• A Singular Problem
• Problems in Polygonal Domains
• Time Discretization by Laplace Transformation and Quadrature.