For a given nonlinear problem discretized by standard finite elements, we propose two iterative schemes to solve the discrete problem. We prove the well-posedness of the corresponding problems and their convergence. Next, we construct error indicators and prove optimal a posteriori estimates where we treat separately the discretization and linearization errors. Some numerical experiments confirm the validity of the schemes and allow us to compare them.
['Christine Bernardi', 'Jad Dakroub', 'Gihane Mansour', 'Farah Rafei', 'Toni Sayah']
Convergence Analysis of Two Numerical Schemes Applied to a Nonlinear Elliptic Problem