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Galerkin Finite Element Methods for Parabolic Problems

✍ Scribed by Vidar Thomée (auth.)

Publisher
Springer-Verlag Berlin Heidelberg
Year
1984
Tongue
English
Leaves
242
Series
Lecture Notes in Mathematics 1054
Edition
1
Category
Library
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✦ Table of Contents

The standard Galerkin method....Pages 1-16
Semidiscrete methods based on more general approximations of the elliptic problem....Pages 17-32
Smooth and non-smooth data error estimates for the homogeneous equation....Pages 33-48
Parabolic equations with more general elliptic operators....Pages 49-61
Maximum-Norm estimates....Pages 62-75
Negative norm estimates and superconvergence....Pages 76-91
Completely discrete schemes for the homogeneous equation....Pages 92-105
Completely discrete schemes for the inhomogeneous equation....Pages 106-125
Time discretization by the discontinuous Galerkin method....Pages 126-148
A nonlinear problem....Pages 149-165
The method of lumped masses....Pages 166-186
The H 1 and H βˆ’1 methods....Pages 187-204
A mixed method....Pages 205-220
A singular problem....Pages 221-235

✦ Subjects

Numerical Analysis

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This book surveys the mathematics of Galerkin finite element method as applied to parabolic equations. The approach is to first discretize in the spatial variables by Galerkin's method, using piecewise polynomial trial functions, and then to apply some time stepping method, most often of single step

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This book surveys the mathematics of Galerkin finite element method as applied to parabolic equations. The approach is to first discretize in the spatial variables by Galerkin's method, using piecewise polynomial trial functions, and then to apply some time stepping method, most often of single step