The recent developments in the research area of computational mechanics and numerical methods have shown a strong focus on enhancing the robustness, efficiency, and accuracy of finite element and discontinuous Galerkin methods. There is a notable trend towards the development of mixed finite element methods that are parameter-robust, addressing issues such as locking phenomena and nearly incompressible regimes. These methods are being applied to a variety of problems, including linear Cosserat elasticity, unsteady Stokes equations, and parameterized stochastic Navier-Stokes flow problems, demonstrating their versatility and effectiveness.

Another significant direction is the pursuit of entropy-stable and non-oscillatory schemes for hyperbolic conservation laws, which aim to control entropy production and suppress spurious oscillations, crucial for accurate simulations of fluid dynamics and structural mechanics. The integration of peridynamic models with classical continuum mechanics to simulate structural failure more efficiently is also gaining traction, offering a promising approach to improve computational efficiency without compromising accuracy.

In the realm of structural dynamics, there is a growing interest in adaptive coupling strategies and the impact of mass lumping on discrete frequencies, particularly in the context of immersogeometric analysis. Additionally, innovative methods for excitation harmonization and dynamic modeling of large deployable mesh reflectors are being developed, addressing practical challenges in structural testing and space applications.

Noteworthy papers include one that proposes a new variational formulation for the Stokes problem using T-coercivity, stabilizing unstable finite element pairs and improving numerical approximations, and another that introduces a mimetic approach for computing divergence-free metric terms in DGSEMs, essential for free-stream preservation and entropy stability on curvilinear grids.