Convergence of an adaptive Ka\vcanov FEM for quasi-linear problems

2010/06/16 by Eduardo M. Garau, Garau, Eduardo M., Pedro Morín +3 · 2 citations
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1006.3319

openalex publication_date 2010/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We design an adaptive finite element method to approximate the solutions of\nquasi-linear elliptic problems. The algorithm is based on a Ka vcanov\niteration and a mesh adaptation step is performed after each linear solve. The\nmethod is thus \inexact because we do not solve the discrete nonlinear\nproblems exactly, but rather perform one iteration of a fixed point method\n(Ka vcanov), using the approximation of the previous mesh as an initial\nguess. The convergence of the method is proved for any \reasonable\nmarking strategy and starting from any initial mesh. We conclude with some\nnumerical experiments that illustrate the theory.\n

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• Newton's method in adaptive iteratively linearized FEM
• Iterative energy reduction Galerkin methods and variational adaptivity

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