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CONVERGENCE ANALYSIS OF TWO NUMERICAL SCHEMES APPLIED TO A NONLINEAR ELLIPTIC PROBLEM

By Christine Bernardi, Jad Dakroub, Gihane Mansour, Farah Rafei and Toni Sayah

Abstract

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

Topics: Linearization methods, A priori and a posteriori analysis, [ INFO.INFO-NA ] Computer Science [cs]/Numerical Analysis [cs.NA]
Publisher: HAL CCSD
Year: 2015
OAI identifier: oai:HAL:hal-01154534v1
Provided by: Hal-Diderot

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