The field of numerical methods for partial differential equations is witnessing significant developments, with a focus on improving the accuracy, efficiency, and robustness of numerical schemes. Recent research has concentrated on designing innovative finite element methods, gradient flow models, and partitioned strategies to tackle complex problems in areas such as optimal control, cardiac electrophysiology, and uncertainty quantification. Noteworthy papers include: the proposal of a monotone finite element method for elliptic distributed optimal control problems, which ensures the preservation of desired-state bounds and stability of the numerical optimal state. the development of a novel bidomain partitioned strategy for simulating ventricular fibrillation dynamics, which achieves high accuracy and efficiency compared to standard decoupled strategies.