Add hess argument to Region(hess=False)

[adtzlr]

The element must provide a hessian-method for Region(hess=True).

• Extend the __repr__ method of Region by hessian evaluated: True
• Add Tests

Hessian-based (HuHu-) Regularization

$$ \Pi = \int_V \frac{1}{2}\ \mathbb{H}(\boldsymbol{u}) \vdots \mathbb{H}(\boldsymbol{u})\ dV $$

see https://en.wikipedia.org/wiki/Third_medium_contact_method

import felupe as fem

mesh = fem.Cube()
region = fem.RegionHexahedron(mesh, hess=True)
displacement = fem.Field(region, dim=3)
field = fem.FieldContainer([displacement])

@fem.Form(v=field, u=field)
def bilinearform():
    return [lambda v, u: dddot(hess(v), hess(u))]

@fem.Form(v=field)
def linearform():
    u = field[0]
    return [lambda v: dddot(hess(v), hess(u))]

matrix = bilinearform.assemble(v=field, u=field)
vector = linearform.assemble(v=field)

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 97.52%. Comparing base (7cabbfd) to head (c182d75).
Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #836      +/-   ##
==========================================
+ Coverage   97.48%   97.52%   +0.04%     
==========================================
  Files         147      147              
  Lines        5601     5665      +64     
==========================================
+ Hits         5460     5525      +65     
+ Misses        141      140       -1     

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