In this paper, we extend the tangential-displacement normal–normal-stress continuous (TDNNS) method from Pechstein and Schöberl (2011) to nonlinear elasticity. By means of Hu–Washizu principle, distributional derivatives displacement vector are lifted a regular strain tensor. We introduce three different methods, where either deformation gradient, Cauchy–Green tensor, or both them used as indep...

We propose a framework for the unified analysis of mixed methods for elasticity with weakly symmetric stress. Based on a commuting diagram in the weakly symmetric elasticity complex and extending a previous stability result, stable mixed methods are obtained by combining Stokes stable and elasticity stable finite elements. We show that the framework can be used to analyze most existing mixed me...

In this work, a two-layer coupled fluid-structure-structure interaction model is considered, which incorporates an anisotropic structure model into the fluid-structure interaction problems. We propose two domain decomposition solvers for such a class of coupled problems: a Robin-Robin preconditioned GMRES solver combined with an inner Dirichlet-Neumann iterative solver, and a Robin-Robin precon...