Finite Element Convergence Analysis of a Schwarz Alternating Method for Nonlinear Elliptic PDEs

Boulbrachene, Messaoud

doi:10.24200/squjs.vol24iss2pp109-121

Cited by 3 publications

(2 citation statements)

References 11 publications

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“…This work introduces a new approach and uses weaker assumptions on the nonlinearity than the one developed in [14] to derive the convergence result.…”

Section: Introductionmentioning

confidence: 99%

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L∞-Convergence Analysis of a Finite Element Linear Schwarz Alternating Method for a Class of Semi-Linear Elliptic PDEs

Farei¹,

Boulbrachene

2023

Int. J. Anal. Appl.

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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.

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“…This work introduces a new approach and uses weaker assumptions on the nonlinearity than the one developed in [14] to derive the convergence result.…”

Section: Introductionmentioning

confidence: 99%

“…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.…”

mentioning

confidence: 99%

L∞-Convergence Analysis of a Finite Element Linear Schwarz Alternating Method for a Class of Semi-Linear Elliptic PDEs

Farei¹,

Boulbrachene

2023

Int. J. Anal. Appl.

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Convergence analysis of non-matching finite elements for a linear monotone additive Schwarz scheme for semi-linear elliptic problems

Al Farei,

Boulbrachene

2024

Nonlinear Engineering

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In this article, we are interested in the standard finite element approximation method of linear additive Schwarz iterations for a class of semi-linear elliptic problems, for two subdomains, in the context of non-matching grids. More precisely, by means of a uniform convergence result from the study by Lui and a fundamental lemma consisting of estimating, at each iteration, the gap between the continuous and the finite element Schwarz iterates, we prove that the discrete Schwarz sequences converge, in the maximum norm, to the true solution. Moreover, we also give numerical results to support the theoretical findings.

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

Farei,

Boulbrachene,

Boulbrachene

2024

DCDS-S

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Finite Element Convergence Analysis of a Schwarz Alternating Method for Nonlinear Elliptic PDEs

Cited by 3 publications

References 11 publications

L∞-Convergence Analysis of a Finite Element Linear Schwarz Alternating Method for a Class of Semi-Linear Elliptic PDEs

L∞-Convergence Analysis of a Finite Element Linear Schwarz Alternating Method for a Class of Semi-Linear Elliptic PDEs

Convergence analysis of non-matching finite elements for a linear monotone additive Schwarz scheme for semi-linear elliptic problems

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

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