A dual-dual formulation for the coupling of mixed-FEM and BEM in
hyperelasticity
Gabriel N. Gatica, Norbert Heuer
SIAM J. Numer. Anal., 38 (2), 380-400, 2000.
We combine a dual-mixed finite element method with the boundary integral
equation method, to study the solvability and Galerkin approximations of a
linear-nonlinear transmission problem arising in plane elastostatics. Our
approach is based on the introduction of the strain tensor as an auxiliary
unknown in the finite element domain, and it leads to what we call a
dual-dual mixed formulation since the corresponding operator equation
becomes
of a two-fold saddle point structure. We derive existence and uniqueness of
solution for the continuous and discrete formulations, and provide the
associated error analysis. In particular, we extend the finite element space
for plane elasticity given by the PEERS element and define an explicit finite
element/boundary element subspace satisfying all the required compatibility
conditions. Most of our analysis makes use of an extension of the classical
Babuska-Brezzi theory to a class of nonlinear saddle-point problems.