Generalized mixed and primal hybrid methods with applications to plate bending
Norbert Heuer
We present an extended framework for hybrid finite element approximations
of self-adjoint, positive definite operators.
It covers the cases of primal, mixed, and ultraweak formulations, both at the
continuous and discrete levels, and gives rise to conforming discretizations.
Our framework allows for flexible continuity restrictions across elements,
and includes the extreme cases of conforming and discontinuous hybrid methods.
We illustrate an application of the framework to the Kirchhoff–Love
plate pending model and present three primal hybrid and two mixed hybrid methods,
four of them with numerical examples. In particular, we present conforming
frameworks for (in classical meaning) non-conforming elements of
Morley, Zienkiewicz triangular, and Hellan–Herrmann–Johnson types.