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Volume 13, Issue 2
A Dynamical Method for Solving the Obstacle Problem

Qinghua Ran, Xiaoliang Cheng & Stéphane Abide

DOI: 10.4208/nmtma.OA-2019-0109

Numer. Math. Theor. Meth. Appl., 13 (2020), pp. 353-371.

Published online: 2020-03

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  • 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.

  • Keywords

Variational inequality, obstacle problem, dynamical system, dynamical functional partical method.

  • AMS Subject Headings

35J86, 65N22, 65N06, 65M06

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

qhran@zju.edu.cn (Qinghua Ran)

stephane.abide@univ-perp.fr (Stéphane Abide)

  • BibTex
  • RIS
  • TXT
@Article{NMTMA-13-353, author = {Ran , QinghuaCheng , Xiaoliang and Abide , Stéphane}, title = {A Dynamical Method for Solving the Obstacle Problem}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2020}, volume = {13}, number = {2}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2019-0109}, url = {http://global-sci.org/intro/article_detail/nmtma/15462.html} }
TY - JOUR T1 - A Dynamical Method for Solving the Obstacle Problem AU - Ran , Qinghua AU - Cheng , Xiaoliang AU - Abide , Stéphane JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 353 EP - 371 PY - 2020 DA - 2020/03 SN - 13 DO - http://doi.org/10.4208/nmtma.OA-2019-0109 UR - https://global-sci.org/intro/article_detail/nmtma/15462.html KW - Variational inequality, obstacle problem, dynamical system, dynamical functional partical method. AB -

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.

Qinghua Ran, Xiaoliang Cheng & Stéphane Abide. (2020). A Dynamical Method for Solving the Obstacle Problem. Numerical Mathematics: Theory, Methods and Applications. 13 (2). 353-371. doi:10.4208/nmtma.OA-2019-0109
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