The field of finite element methods is moving towards addressing complex problems with non-standard boundary conditions and mixed boundary conditions. Researchers are developing new schemes and analyzing their properties to ensure locking-free and optimal rates of convergence. The de Rham complex is being utilized to guide the development of these schemes. Additionally, there is a focus on structure-preserving approximations, which aim to conserve physical quantities such as mass, internal energy, and entropy. The analysis of mixed finite element methods for problems with rough boundary data is also a growing area of research. Noteworthy papers include:

• A study on locking-free finite element schemes for holey Reissner-Mindlin plates, which provides conditions for schemes to deliver optimal rates of convergence.
• A paper on a mixed Petrov--Galerkin Cosserat rod finite element formulation, which presents a computationally efficient approach for analyzing Cosserat rods that is free of singularities and locking.