We propose four multipoint stress mixed finite element methods for the linear Cosserat equations that are stable in the limit of linear elasticity.
- The first two methods employ $BDM_1$ elements for the stress variables, and we propose two higher-order methods using $RT_1$ elements.
- Linear convergence is proven for all methods using a priori error estimates.
- For the methods based on $RT_1$ elements, we show quadratic convergence in some of the variables.
- Numerical experiments in 2D and 3D confirm the theoretical findings and we even observe higher orders of convergence than expected.