Work

Mixing finite-element and finite-difference discretizations in linear monotone Schwarz iterations for semilinear elliptic PDEs

Year: 2024

Type: article

Abstract: In this paper, we are concerned with a mixed finite-element and finite-difference (FEM-FDM) approximation method of linear Schwarz alternating iterations for a class of semilinear elliptic PDEs.More precisely, we consider two overlapping sub-domains $ \Omega_{1} $ and $ \Omega_{2} $, discretized by FEM-FDM, respectively, in the context of non-matching grids in the overlapping region. In this situation, combining a convergence result due to S.H. Lui [18] and a fundamental lemma consisting of estimating the gap between the continuous and discrete Schwarz iterations, we prove that the corresponding discrete Schwarz iterations converge uniformly to the true solution on $ \Omega_{1} $ and $ \Omega_{2} $, respectively. We also give some numerical results to support the theory.

Source: Discrete and Continuous Dynamical Systems - S

DOI: 10.3934/dcdss.2024140

Authors: Qais Al Farei, Khaled Boulbrachene, Messaoud Boulbrachene

Institutions: Sultan Qaboos University, Universität Hamburg, Helmut Schmidt University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4401461267

FWCI:

Cites: 14

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Related to: 10