NAME¶

2D -- rate of deformation tensor

SYNOPSIS¶

        form (const space V, const space& T, "2D");
 

DESCRIPTION¶

Assembly the form associated to the rate of deformation tensor, i.e. the symmetric part of the gradient of a vector field. These derivative are usefull in fluid mechanic and elasticity.

                 /
                 |
      b(u,tau) = | 2 D(u) : tau dx,
                 |
                 / Omega
 

where

     2 D(u) = grad u + (grad u)^T
 

If the V space is a vector-valued P1 (resp. P2) finite element space, the T space may be a tensor-valued P0 (resp. P1d) one.

EXAMPLE¶

The following piece of code build the Laplacian form associated to the P1 approximation:

        geo omega ("square");
        space V (omega, "P1", "vector");
        space T (omega, "P0", "tensor");
        form  b (V, T, "2D");