Abstract:We study an iterative Galerkin method for quasilinear elliptic problems in the Browder-Minty setting. The resulting discrete nonlinear systems are solved by linearization via a (damped) Zarantonello iteration. Unlike prior work, adaptive mesh refinement is driven by an elliptic reconstruction error estimator, which is natural in the sense that the a posteriori bounds for the linearization and discretization errors are well separated. For this setting, we present the first comprehensive convergence analysis of the corresponding algorithm. We prove unconditional full R-linear convergence of a suitable quasi-error that combines linearization and discretization errors. For sufficiently small adaptivity parameters, we further establish optimal convergence rates with respect to the number of degrees of freedom and quasi-optimal complexity, i.e., optimal convergence rates with respect to the overall computational cost. Numerical experiments underpin the theoretical findings.
| Subjects: | Numerical Analysis (math.NA) |
| MSC classes: | 65N30, 65N50, 65N15, 65Y20, 41A25 |
| Cite as: | arXiv:2605.20057 [math.NA] |
| (or arXiv:2605.20057v2 [math.NA] for this version) | |
| https://doi.org/10.48550/arXiv.2605.20057 arXiv-issued DOI via DataCite |
From: Christoph Lietz [view email]
[v1]
Tue, 19 May 2026 16:15:13 UTC (459 KB)
[v2]
Fri, 22 May 2026 07:33:51 UTC (459 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。