Ebook: The Mathematical Theory of Finite Element Methods

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Content:
Front Matter....Pages i-xv
Basic Concepts....Pages 1-21
Sobolev Spaces....Pages 23-47
Variational Formulation of Elliptic Boundary Value Problems....Pages 49-67
The Construction of a Finite Element Space....Pages 69-92
Polynomial Approximation Theory in Sobolev Spaces....Pages 93-127
n-Dimensional Variational Problems....Pages 129-154
Finite Element Multigrid Methods....Pages 155-173
Additive Schwarz Preconditioners....Pages 175-208
Max-norm Estimates....Pages 209-234
Adaptive Meshes....Pages 235-255
Variational Crimes....Pages 257-278
Applications to Planar Elasticity....Pages 279-297
Mixed Methods....Pages 299-322
Iterative Techniques for Mixed Methods....Pages 323-338
Applications of Operator-Interpolation Theory....Pages 339-348
Back Matter....Pages 349-363

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Content:
Front Matter....Pages i-xv
Basic Concepts....Pages 1-21
Sobolev Spaces....Pages 23-47
Variational Formulation of Elliptic Boundary Value Problems....Pages 49-67
The Construction of a Finite Element Space....Pages 69-92
Polynomial Approximation Theory in Sobolev Spaces....Pages 93-127
n-Dimensional Variational Problems....Pages 129-154
Finite Element Multigrid Methods....Pages 155-173
Additive Schwarz Preconditioners....Pages 175-208
Max-norm Estimates....Pages 209-234
Adaptive Meshes....Pages 235-255
Variational Crimes....Pages 257-278
Applications to Planar Elasticity....Pages 279-297
Mixed Methods....Pages 299-322
Iterative Techniques for Mixed Methods....Pages 323-338
Applications of Operator-Interpolation Theory....Pages 339-348
Back Matter....Pages 349-363
....