Finite Elements III : First-Order and Time-Dependent PDEs /
This book is the third volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exer...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Cham :
Springer International Publishing : Imprint: Springer,
2021.
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| Edition: | 1st ed. 2021. |
| Series: | Texts in Applied Mathematics,
74 |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Part XII: First-order PDEs
- Friedrichs' systems
- Residual-based stabilization
- Fluctuation-based stabilization (I)
- Fluctuation-based stabilization (II)
- Discontinuous Galerkin
- Advection-diffusion
- Stokes equations: Residual-based stabilization-. Stokes equations: other stabilizations
- Part XIII: Parabolic PDEs
- Bochner integration
- Weak integration and well-posedness
- Semi-discretization in space
- Implicit and explicit Euler schemes
- BDF2 and Crank-Nicolson schemes
- Discontinuous Galerkin in time
- Continuous Petrov-Galerkin in time
- Analysis using inf-sup stability
- Part XIV: Time-dependent Stokes equations
- Weak formulations and well-posedness
- Monolithic time discretization
- Projection methods
- Artificial compressibility
- Part XV: Time-dependent first-order linear PDEs
- Well-posedness and space semi-discretization
- Implicit time discretization
- Explicit time discretization
- Part XVI: Nonlinear hyperbolic PDEs
- Scalar conservation equations
- Hyperbolic systems
- First-order approximation
- Higher-order approximation
- Higher-order approximation and limiting.