NAME¶

test, trial - symbolic arguments in variational expressions

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 test type represents the formal argument (the test-function) in the definition of a linear form, as in:

    geo omega ("circle");
    space Xh (omega, "P1");
    test v(Xh);
    field lh = integrate (omega, 2*v);

For a bilinear form, the test-function represents its second formal argument, while the first one is designed by the trial type:

    trial u(Xh);
    test  v(Xh);
    form m = integrate (omega, u*v),
         a = integrate (omega, dot(grad(u),grad(v)));

The field_vf class is abble to represents either test or trial types: it could be used to formaly define a differential operator, as:

    D(u) = (grad(u)+trans(grad(u)))