In this paper, we are concerned with a nonmatching grid mixed finite-elements–finite-differences approximation (FEM-FD) method of overlapping nonlinear multiplicative Schwarz iterations for nonlinear elliptic PDEs. By means of a geometric convergence result in L∞ for the nonlinear Schwarz iterations and a Lipschitz property with respect to the data of both the FEM and FD solutions of the corresponding linear PDE problems, we derive an L∞ error estimate on each subdomain between the discrete nth Schwarz iterate and the true solution of the nonlinear PDE.
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Al Farei, Q., Boulbrachene, M. Mixing Finite Elements and Finite Differences in Nonlinear Schwarz Iterations for Nonlinear Elliptic Pdes. Comput Math Model 33, 77–94 (2022). https://doi.org/10.1007/s10598-022-09558-x
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DOI: https://doi.org/10.1007/s10598-022-09558-x