.\"
.de Id
..
.de Sp
.if n .sp
.if t .sp 0.4
..
.TH test 2rheolef "rheolef-6.7" "rheolef-6.7" "rheolef-6.7"
.\" label: /*Class:field_vf
.SH NAME
\fBtest\fP, \fBtrial\fP - symbolic arguments in variational expressions
.SH DESCRIPTION

These classes are used for test and trial functions
involved in variational formulations.
Variational formulations could be specified by expressions, in
the spirit of c++ embeded languages.
A variable of the \fBtest\fP type represents the formal argument
(the test-function) in the definition of a linear form, as in:
.\" begin_example
.Sp
.nf
    geo omega ("circle");
    space Xh (omega, "P1");
    test v(Xh);
    field lh = integrate (omega, 2*v);
.Sp
.fi
.\" end_example
For a bilinear form, the test-function represents its second formal argument,
while the first one is designed by the \fBtrial\fP type:
.\" begin_example
.Sp
.nf
    trial u(Xh);
    test  v(Xh);
    form m = integrate (omega, u*v),
         a = integrate (omega, dot(grad(u),grad(v)));
.Sp
.fi
.\" end_example
The \fBfield_vf\fP class is abble to represents either \fBtest\fP or
\fBtrial\fP types: it could be used to formaly define a differential
operator, as:
.\" begin_example
.Sp
.nf
    D(u) = (grad(u)+trans(grad(u)))
.Sp
.fi
.\" end_example
.\" END