The field of numerical methods for elasticity and contact problems is witnessing significant advancements, with a focus on developing innovative and robust techniques to tackle complex problems. Recent work has concentrated on addressing longstanding issues such as locking and non-robustness in finite element methods, with novel approaches including parameter-free and locking-free enriched Galerkin methods and physics-informed neural networks. These new methods have shown promising results in terms of accuracy, efficiency, and robustness. Additionally, there has been progress in the development of reduced-order models for dynamic contact problems and the application of Trefftz discontinuous Galerkin methods to scattering problems. Noteworthy papers include:

• A novel parameter-free and locking-free enriched Galerkin method for linear elasticity, which delivers an oscillation-free stress approximation without requiring post-processing.
• A physics-informed neural network approach for solving nearly incompressible elasticity equations, which alleviates the extreme imbalance in the coefficients and recovers the solutions of the decomposed systems as well as the associated external conditions.