# Term Overview¶

## Term Syntax¶

In general, the syntax of a term call is:

<term name>.<i>.<r>( <arg1>, <arg2>, ... ),

where <i> denotes an integral name (i.e. a name of numerical quadrature to use) and <r> marks a region (domain of the integral).

The following notation is used:

Notation.

symbol

meaning

volume (sub)domain

surface (sub)domain

volume or surface (sub)domain

dimension of space

time

any function

any vector function

unit outward normal

,

scalar test function

,

scalar unknown or parameter function

scalar parameter function

vector test function

,

vector unknown or parameter function

vector parameter function

Cauchy strain tensor ()

right Cauchy-Green deformation tensor

Green strain tensor

second Piola-Kirchhoff stress tensor

vector volume forces

scalar volume force (source)

density

kinematic viscosity

any constant

Kronecker delta, identity matrix

trace of a second order tensor ()

deviator of a second order tensor ()

-th element of triangulation (= mesh) of domain

is assigned values from in ascending order

The suffix “” denotes a quantity related to a previous time step.

Term names are (usually) prefixed according to the following conventions:

Term name prefixes.

prefix

meaning

evaluation modes

meaning

dw

discrete weak

‘weak’

terms having a virtual (test) argument and zero or more unknown arguments, used for FE assembling

ev

evaluate

‘eval’, ‘el_eval’, ‘el_avg’, ‘qp’

terms having all arguments known, modes ‘el_avg’, ‘qp’ are not supported by all ev_ terms

de

discrete einsum

any (work in progress)

multi-linear terms defined using an enriched einsum notation

## Term Table¶

Below we list all the terms available in automatically generated tables. The first column lists the name, the second column the argument lists and the third column the mathematical definition of each term. The terms are devided into the following tables:

The notation <virtual> corresponds to a test function, <state> to a unknown function and <parameter> to a known function. By <material> we denote material (constitutive) parameters, or, in general, any given function of space and time that parameterizes a term, for example a given traction force vector.