Convergence Analysis of Two Numerical Schemes Applied to a Nonlinear Elliptic Problem
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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.
KeywordsPosteriori error estimation Nonlinear problems Iterative methods Finite elements method