The fields of numerical methods for elasticity and contact problems, partial differential equations, shallow water modeling, and power grid research are experiencing significant developments. A common theme among these areas is the focus on innovative and robust techniques to tackle complex problems. In elasticity and contact problems, novel approaches such as parameter-free and locking-free enriched Galerkin methods and physics-informed neural networks have shown promising results. For partial differential equations, adaptive and asymptotic-preserving schemes, such as the zigzag schemes, have improved stability and accuracy. Shallow water modeling has seen the development of locally adaptive non-hydrostatic models and hyperbolic regularization techniques, reducing computational time while maintaining accuracy. The integration of deep learning techniques in partial differential equations has also shown promising results, with methods such as the Spectral-inspired Neural Operator and KITINet enabling efficient and accurate solutions. In power grid research, new frameworks and approaches are being explored to address grid stability and optimization challenges. Noteworthy papers include a novel parameter-free and locking-free enriched Galerkin method for linear elasticity, an adaptive-rank approach for simulating multi-scale BGK equations, and a dynamic phasor framework for analyzing grid-forming converters. These advancements have the potential to greatly impact various fields, including engineering, physics, and biology, by enabling more accurate and efficient simulations of complex systems.