Finite Elements II : Galerkin Approximation, Elliptic and Mixed PDEs /
This book is the second 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 exe...
| 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,
73 |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Part V: Weak formulations and well-posedness
- Weak formulation of model problems
- Main results on well-posedness
- Part VI: Galerkin approximation
- Basic error analysis
- Error analysis with variational crimes
- Linear algebra
- Sparse matrices
- Quadratures
- Part VII: Elliptic PDEs: conforming approximation
- Scalar second-order elliptic PDEs
- H1-conforming approximation (I)
- H1-conforming approximation (II)
- A posteriori error analysis
- The Helmholtz problem
- Part VIII: Elliptic PDEs: nonconforming approximation
- Crouzeix-Raviart approximation
- Nitsche's boundary penalty method
- Discontinuous Galerkin
- Hybrid high-order methods
- Contrasted diffusivity (I)
- Contrasted diffusivity (II)
- Part IX: Vector-valued elliptic PDEs
- Linear elasticity
- Maxwell's equations: H(curl)-approximation
- Maxwell's equations: control on the divergence
- Maxwell's equations: further topics
- Part X: Eigenvalue problems
- Symmetric elliptic eigenvalue problems
- Symmetric operators, conforming approximation
- Nonsymmetric problems
- Part XI: PDEs in mixed form
- Well-posedness for PDEs in mixed form
- Mixed finite element approximation
- Darcy's equations
- Potential and flux recovery
- Stokes equations: Basic ideas
- Stokes equations: Stable Pairs (I)
- Stokes equations: Stable pairs (II)
- Appendices
- Bijective operators in Banach spaces.