A Dynamical Method for Solving the Obstacle Problem

A Dynamical Method for Solving the Obstacle Problem

Year:    2020

Author:    Stéphane Abide, Qinghua Ran, Xiaoliang Cheng, Stéphane Abide

Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 2 : pp. 353–371

Abstract

In this paper, we consider the unilateral obstacle problem, trying to find the numerical solution and coincidence set. We construct an equivalent format of the original problem and  propose a method with a second-order in time dissipative system for solving the equivalent format. Several numerical examples are given to illustrate the effectiveness and stability of the proposed algorithm. Convergence speed comparisons with existent numerical algorithm are also provided and our algorithm is fast.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2019-0109

Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 2 : pp. 353–371

Published online:    2020-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    Variational inequality obstacle problem dynamical system dynamical functional partical method.

Author Details

Stéphane Abide

Qinghua Ran

Xiaoliang Cheng

Stéphane Abide

  1. Analysis of a new kind of elastic-rigid bilateral obstacle problem

    Zhang, Jie | Ran, Qinghua

    Mathematics and Mechanics of Solids, Vol. 28 (2023), Iss. 12 P.2661

    https://doi.org/10.1177/10812865231172425 [Citations: 1]
  2. Optimal control of an elastic–rigid obstacle problem

    Ran, Qinghua | Zhang, Jie

    Communications in Nonlinear Science and Numerical Simulation, Vol. 132 (2024), Iss. P.107935

    https://doi.org/10.1016/j.cnsns.2024.107935 [Citations: 0]
  3. Proceedings of Academia-Industry Consortium for Data Science

    A Deep Learning Approach for the Obstacle Problem

    Darehmiraki, Majid

    2022

    https://doi.org/10.1007/978-981-16-6887-6_16 [Citations: 0]
  4. Numerical analysis for a new kind of obstacle problem

    Cheng, Xiaoliang | Ran, Qinghua | Wang, Xilu | Xiao, Qichang

    Communications in Nonlinear Science and Numerical Simulation, Vol. 99 (2021), Iss. P.105810

    https://doi.org/10.1016/j.cnsns.2021.105810 [Citations: 4]
  5. A dynamical method for optimal control of the obstacle problem

    Ran, Qinghua | Cheng, Xiaoliang | Gong, Rongfang | Zhang, Ye

    Journal of Inverse and Ill-posed Problems, Vol. 0 (2023), Iss. 0

    https://doi.org/10.1515/jiip-2020-0135 [Citations: 1]