TY - JOUR
T1 - Mixing Finite Elements and Finite Differences in Nonlinear Schwarz Iterations for Nonlinear Elliptic Pdes
AU - Al Farei, Qais
AU - Boulbrachene, Messaoud
N1 - Publisher Copyright:
© 2022, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2022/1/1
Y1 - 2022/1/1
N2 - 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.
AB - 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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UR - https://www.mendeley.com/catalogue/f071a88e-ed0d-3a6a-bae1-ab10d48c4c79/
U2 - 10.1007/s10598-022-09558-x
DO - 10.1007/s10598-022-09558-x
M3 - Article
AN - SCOPUS:85135459659
SN - 1046-283X
VL - 33
SP - 77
EP - 94
JO - Computational Mathematics and Modeling
JF - Computational Mathematics and Modeling
IS - 1
ER -