Application of the meshless interpolating element-free Galerkin method for the numerical solution of obstacle problem

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran.

2 Department of Mathematics, College of Computer and Mathematics, University of Thi-Qar, Iraq.

Abstract

The obstacle problem is a speci fic type of contact problem that can be formulated
as a variational inequality or complementary problem in function
spaces. Such problems often yield non-smooth solutions, making it challenging
to fi nd a suitable numerical approximation. In this paper, we present a
meshfree method for numerically solving an obstacle problem. In proposed
method the interpolating moving least square approximation is utilized in
element-free Galerkin approach. Implementing this method on a computer
is straightforward and effective. To ensure the effciency of the proposed
method, we have investigated the convergent of the proposed method . Additionally,
we have solved several examples of the obstacle problem using the
proposed method. The numerical results obtained con firm the theoretical
achievements and demonstrate the method's effectiveness and accuracy.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 01 September 2025

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History

  • Receive Date: 08 December 2024
  • Revise Date: 21 May 2025
  • Accept Date: 01 September 2025

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