Deep learning-based numerical schemes such as Physically Informed Neural Networks (PINNs) have recently emerged an alternative to classical for solving Partial Differential Equations (PDEs). They are very appealing at first sight because implementing vanilla versions of PINNs based on strong residual forms is easy, and neural networks offer high approximation capabilities. However, when the PDE...

Finite diierence schemes for singularly perturbed convection problems are studied in the limit case in which the viscosity approaches zero with the mesh-size. The error estimates allow choosing in advance appropriate schemes and mesh-resolutions for both boundary layer problems and circulating ow problems.