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1.

電子ブック
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1. Mathematical Aspects of Discontinuous Galerkin Methods
by Daniele Antonio Di Pietro, Alexandre Ern
出版情報: Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2012
シリーズ名: Mathématiques et Applications ; 69
オンライン: http://dx.doi.org/10.1007/978-3-642-22980-0
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2.

電子ブック
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2. Finite Elements I : Approximation and Interpolation. 1st ed. 2021
by Alexandre Ern, Jean-Luc Guermond
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2021
シリーズ名: Texts in Applied Mathematics ; 72
オンライン: https://doi.org/10.1007/978-3-030-56341-7
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目次情報: 続きを見る
Part I: Elements of Functional Analysis
Lebesgue spaces
Weak derivatives and Sobolev spaces
Traces and Poincaré Inequalities
Duality in Sobolev spaces
Part II: Introduction to Finite Elements
Main ideas and definitions
One-dimensional finite elements and tensorization
Simplicial finite elements
Part III: Finite element interpolation
Meshes
Finite element generation
Mesh orientation
Local interpolation on affine meshes
Local inverse and functional inequalities
Local interpolation on non-affine meshes
H(div) finite elements
H(curl) finite elements
Local interpolation in H(div) and H(curl) (I)
Local interpolation in H(div) and H(curl) (II)
Part IV: Finite element spaces
From broken to conforming spaces
Main properties of the conforming spaces
Face gluing
Construction of the connectivity classes
Quasi-interpolation and best approximation
Commuting quasi-interpolation
Appendices
Banach and Hillbert spaces
Differential calculus
Part I: Elements of Functional Analysis
Lebesgue spaces
Weak derivatives and Sobolev spaces
3.

電子ブック
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3. Hybrid High-Order Methods : A Primer with Applications to Solid Mechanics. 1st ed. 2021
by Matteo Cicuttin, Alexandre Ern, Nicolas Pignet
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2021
シリーズ名: SpringerBriefs in Mathematics ;
オンライン: https://doi.org/10.1007/978-3-030-81477-9
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1.Getting Started: Linear Diffusion
2.Mathematical Aspects
3.Some Variants
4.Linear Elasticity and Hyperelasticity
5.Elastodynamics
6.Contact and Friction
7.Plasticity
8.Implementaion Aspects
References
1.Getting Started: Linear Diffusion
2.Mathematical Aspects
3.Some Variants
4.

電子ブック
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4. Finite Elements II : Galerkin Approximation, Elliptic and Mixed PDEs. 1st ed. 2021
by Alexandre Ern, Jean-Luc Guermond
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2021
シリーズ名: Texts in Applied Mathematics ; 73
オンライン: https://doi.org/10.1007/978-3-030-56923-5
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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
Part V: Weak formulations and well-posedness
Weak formulation of model problems
Main results on well-posedness
5.

電子ブック
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5. Finite Elements III : First-Order and Time-Dependent PDEs. 1st ed. 2021
by Alexandre Ern, Jean-Luc Guermond
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2021
シリーズ名: Texts in Applied Mathematics ; 74
オンライン: https://doi.org/10.1007/978-3-030-57348-5
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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
Part XII: First-order PDEs
Friedrichs' systems
Residual-based stabilization