Ebook: Galerkin Finite Element Methods for Parabolic Problems

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Content:
Front Matter....Pages I-X
The Standard Galerkin Method....Pages 1-22
Methods Based on More General Approximations of the Elliptic Problem....Pages 23-34
Nonsmooth Data Error Estimates....Pages 35-50
More General Parabolic Equations....Pages 51-62
Maximum-Norm Stability and Error Estimates....Pages 63-80
Negative Norm Estimates and Superconvergence....Pages 81-94
Single Step Fully Discrete Schemes for the Homogeneous Equation....Pages 95-110
Single Step Methods and Rational Approximations of Semigroups....Pages 111-125
Single Step Fully Discrete Schemes for the Inhomogeneous Equation....Pages 127-144
Multistep Backward Difference Methods....Pages 145-162
Incomplete Iterative Solution of the Algebraic Systems at the Time Levels....Pages 163-179
The Discontinuous Galerkin Time Stepping Method....Pages 181-208
A Nonlinear Problem....Pages 209-222
Semilinear Parabolic Equations....Pages 223-238
The Method of Lumped Masses....Pages 239-252
The H 1 and H -1 Methods....Pages 253-266
A Mixed Method....Pages 267-278
A Singular Problem....Pages 279-287
Back Matter....Pages 289-302

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Content:
Front Matter....Pages I-X
The Standard Galerkin Method....Pages 1-22
Methods Based on More General Approximations of the Elliptic Problem....Pages 23-34
Nonsmooth Data Error Estimates....Pages 35-50
More General Parabolic Equations....Pages 51-62
Maximum-Norm Stability and Error Estimates....Pages 63-80
Negative Norm Estimates and Superconvergence....Pages 81-94
Single Step Fully Discrete Schemes for the Homogeneous Equation....Pages 95-110
Single Step Methods and Rational Approximations of Semigroups....Pages 111-125
Single Step Fully Discrete Schemes for the Inhomogeneous Equation....Pages 127-144
Multistep Backward Difference Methods....Pages 145-162
Incomplete Iterative Solution of the Algebraic Systems at the Time Levels....Pages 163-179
The Discontinuous Galerkin Time Stepping Method....Pages 181-208
A Nonlinear Problem....Pages 209-222
Semilinear Parabolic Equations....Pages 223-238
The Method of Lumped Masses....Pages 239-252
The H 1 and H -1 Methods....Pages 253-266
A Mixed Method....Pages 267-278
A Singular Problem....Pages 279-287
Back Matter....Pages 289-302
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