Join a SIAM Geosciences webinar exploring advanced mathematical approaches for handling nonsmooth and degenerate problems in porous media flow and transport. Discover how to overcome convergence challenges in iterative linearization schemes through an innovative epsilon-parametrized approach that maintains the Newton method while adapting regularization parameters. Learn about practical applications in the Richards equation, two-phase flows, and multiphase multicompositional flows, with detailed discussions on handling phase transitions. Examine how this methodology provides certified error estimates while ensuring optimal balance between linearization, regularization, and discretization errors. Gain insights into solving complex mathematical challenges in geosciences, environmental science, and applied mathematics through real-world numerical examples and comprehensive theoretical framework.