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Update ex20_third-medium-contact.py
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adtzlr committed Sep 12, 2024
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# %%
# The so-called HuHu-regularization is created by two weak-:func:`form <felupe.Form>`
# expressions, see Eq. :eq:`huhu-regularization` [3]_.
# The so-called HuHu-regularization is created by two weak-:func:`forms <felupe.Form>`,
# which are derived from the regularization potential, see Eq.
# :eq:`huhu-regularization` [3]_.
#
# .. math::
# :label: huhu-regularization
#
# \Pi &= \frac{1}{2} \int_V
# \Pi = \frac{1}{2} \int_V
# \mathbb{H}(\boldsymbol{u})~\vdots~\mathbb{H}(\boldsymbol{u})~dV
#
# \delta \Pi &= \int_V
# \mathbb{H}(\delta \boldsymbol{u})~\vdots~\mathbb{H}(\boldsymbol{u})~dV
#
# \Delta \delta \Pi &= \int_V
# \mathbb{H}(\delta \boldsymbol{u})~\vdots~\mathbb{H}(\Delta \boldsymbol{u})~dV
#
from felupe.math import dddot, hess


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