Glossary
================

.. hlist::

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     .. _glos.Banach:
     .. admonition:: Banach space
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       This is a complete space equipped with a norm.
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     .. _glos.divtensor:
     .. admonition:: Divergence (of a tensor)
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       Let $\sigma: \Omega \to \R^{d\times d}$ be a second-order tensor, i.e. a matrix-valued mapping on $\Omega$. 
       The divergence of $\sigma$ is the vector field $\dv\sigma : \Omega \to \R^d$ with entries: 
       
       $$(\dv\sigma(\x))_i = \sum\limits_{j=1}^d \frac{\partial \sigma_{ij}}{\partial x_j}(\x), \quad i=1,\ldots,d.$$
        
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     .. _glos.Eulerian:
     .. admonition:: Eulerian (viewpoint)
       :class: dropdown
    
       The Eulerian description of a medium...
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     .. _glos.Frobenius:
     .. admonition:: Frobenius inner product
       :class: dropdown
    
       The Frobenius inner product between two square matrices $M, N \in \mathbb{R}^{d\times d}$ is the real value $M:N$ defined by:
       $$M:N = \text{tr}(M^TN) = \sum\limits_{i,j=1}^d m_{ij} n_{ij}.$$
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     .. _glos.Hilbert:
     .. admonition:: Hilbert space
       :class: dropdown
    
       A Hilbert space is, in particular a Banach space.
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     .. _glos.Lagrangian:
     .. admonition:: Lagrangian (viewpoint)
       :class: dropdown
    
       The Lagrangian description of a medium...
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     .. _glos.LSM:
     .. admonition:: Level set method
       :class: dropdown
    
       The level set method generally consists in representing a domain $\Omega \subset \R^d$ in an implicit way when dealing with its evolution, i.e.
       
       This method is more extensively described in :numref:`sec.LSM`.
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     .. _glos.curvature:
     .. admonition:: Mean curvature
       :class: dropdown
    
       We refer to :numref:`sec.curvature` for further details.
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     .. _glos.strain:
     .. admonition:: Strain
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       Strain is synonymous to deformation.
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     .. _glos.VI:
     .. admonition:: Variational inequality
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       A variational inequality is
       Prototypes are obstacle problems, or contact problems.
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     .. _glos.VP:
     .. admonition::  Variational problem
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       A variational problem is defined by
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     .. _glos.vorticity:
     .. admonition::  Vorticity
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       The vorticity of a fluid is the trend to create eddies.
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