Abstract
In this paper, we prove uniform convergence of the standard finite element method for a Schwarz alternating procedure for a class of semi-linear elliptic partial differential equations, in the context of linear iterations and non-matching grids. More precisely, making use of the subsolution-based concept, we prove that finite element Schwarz iterations converge, in the maximum norm, to the true solution of the PDE. We also give numerical results to validate the theory. This work introduces a new approach and generalizes the one in [14] as it encompasses a larger class of problems.
Original language | English |
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Article number | 71 |
Journal | International Journal of Analysis and Applications |
Volume | 21 |
DOIs | |
Publication status | Published - Jul 17 2023 |
Keywords
- Schwarz method
- finite elements
- non-matching grids
- subsolutions
- uniform convergence
ASJC Scopus subject areas
- Analysis
- Business and International Management
- Geometry and Topology
- Applied Mathematics