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- Title
Adaptive Multi-level Algorithm for a Class of Nonlinear Problems.
- Authors
Kim, Dongho; Park, Eun-Jae; Seo, Boyoon
- Abstract
In this article, we propose an adaptive mesh-refining based on the multi-level algorithm and derive a unified a posteriori error estimate for a class of nonlinear problems. We have shown that the multi-level algorithm on adaptive meshes retains quadratic convergence of Newton's method across different mesh levels, which is numerically validated. Our framework facilitates to use the general theory established for a linear problem associated with given nonlinear equations. In particular, existing a posteriori error estimates for the linear problem can be utilized to find reliable error estimators for the given nonlinear problem. As applications of our theory, we consider the pseudostress-velocity formulation of Navier–Stokes equations and the standard Galerkin formulation of semilinear elliptic equations. Reliable and efficient a posteriori error estimators for both approximations are derived. Finally, several numerical examples are presented to test the performance of the algorithm and validity of the theory developed.
- Subjects
NONLINEAR equations; NEWTON-Raphson method; SEMILINEAR elliptic equations; NAVIER-Stokes equations; ALGORITHMS; TEST validity
- Publication
Computational Methods in Applied Mathematics, 2024, Vol 24, Issue 3, p747
- ISSN
1609-4840
- Publication type
Article
- DOI
10.1515/cmam-2023-0088