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- University
- Politecnico di Milano
- Degree programme
- Aerospace Engineering
- Subject
- Numerical Modeling of Differential Problems
- Classification
- Notes · By topic
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Hyperbolic problems
Study material for Numerical Modeling of Differential Problems, shared by the Studwiz community and reviewed by moderators.
Numerical Modeling of Differential ProblemsBy topic
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Study material for Numerical Modeling of Differential Problems, shared by the Studwiz community and reviewed by moderators.
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Page 1
Contents F oreword................................................... ... V I Basic Material 1 Some fundamental tools for the analysis of PDEs .............. 3 1.1 Lebesgue measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Hilbert spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4 The spaces Lp and H s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.5 Sequences in lp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.6 Important inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2 F undamentals of finite elements ................................ 15 2.1 The one dimensional case: approximation by piecewise po lynomials 15 2.2 Interpolation in higher dimension using finite elements . . . . . . . . . . . 20 2.3 The finite element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.3.1 The degrees of freedom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.3.2 Local and global numbering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.3.3 The reference element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.3.4 Lagrangian finite elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.4 Parametric Finite Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.5 Function approximation by finite elements . . . . . . . . . . . . . . . . . . . . . . 41 II Stationary Problems 3 Galerkin-finite element…
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