The field of numerical methods for partial differential equations is moving towards the development of more efficient and accurate algorithms for solving complex problems. Researchers are focusing on improving existing methods, such as the finite element method, and exploring new approaches, like the use of rational approximations and localized Fourier extensions. These innovations have the potential to significantly impact various applications, including optics, ophthalmology, and wave scattering. Notable papers in this area include: An adaptive multimesh rational approximation scheme for the spectral fractional Laplacian, which demonstrates improved convergence rates and reduced computational costs. A Local Fourier Extension Method for Function Approximation, which achieves spectral accuracy with minimal computational complexity. Sampling patterns for Zernike-like bases in non-standard geometries, which enables stable high-order interpolation and effective wavefront modeling in complex optical systems.