Year: 2025
Type: preprint
Abstract: This paper presents a unified Least-Squares framework for solving nonlinear partial differential equations by recasting the governing system as a residual minimisation problem. A Least-Squares functional is formulated and the corresponding Gauss-Newton method derived, which approximates simultaneously primal and dual variables. We derive conditions under which the Least-Squares functional is coercive and continuous in an appropriate solution space, and establish convergence results while demonstrating that the functional serves as a reliable a posteriori error estimator. This inherent error estimation property is then exploited to drive adaptive mesh refinement across a variety of problems, including the stationary heat equation with either temperature-dependent or discontinuous conductivity, nonlinear elasticity based on the Saint-Venant Kirchhoff model and sea-ice dynamics.
Source: arXiv (Cornell University)
Authors: Bertrand, Fleurianne, Brodbeck, Maximilian, Ricken, Tim, Schneider, Henrik
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979325448
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