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Multigrid methods for non coercive variational inequalities

Yıl 2024, Cilt: 73 Sayı: 1, 222 - 234, 16.03.2024

Nour El Houda Nesba Mohammed Beggas

https://doi.org/10.31801/cfsuasmas.1225525

Öz

In this study, our examination centers around the numerical resolution of non-coercive issues using a multi-grid approach. Our particular emphasis is directed towards employing multi-grid methodologies to tackle non-linear variational inequalities. Our primary goal involves confirming the consistent convergence of the multi-grid algorithm. To attain this objective, we make use of fundamental sub-differential calculus and glean insights from the convergence principles of non-linear multi-grid techniques.

Anahtar Kelimeler

Multigrid method variational inequality finite element iterative method HJB equation non coercive operator

Kaynakça

  • Boulbrachene, M., Haiour, M., The finite element approximation of Hamilton-Jacobi- Bellman equations, Computers & Mathematics with Applications, 41(7-8) (2001), 993–1007. https://www.sciencedirect.com/science/article/pii/S0898122100003345
  • Brezzi, F., Caffarelli, L. A., Convergence of the discrete free boundary for finite element approximations, R.A.I.R.O Anal. Numer., 17 (1983), 385-395. https://eudml.org/doc/193422
  • Ciarlet, P-G., Raviart, P-A., Maximum principle and uniform convergence for the finite element method, Computer Methods in Applied Mechanics and Engineering, 2(1) (1973), 17–31. https://doi.org/10.1016/0045-7825(73)90019-4
  • Cortey-Dumont, P., On the finite element approximation in the $L^{\infty}$ norm of variational inequalities with nonlinear operators, Numer.Num., 47 (1985), 45-57. https://eudml.org/doc/133022
  • Cortey-Dumont, P., Sur I’analyse num´erique des equations de Hamilton-Jacobi-Bellman, Mathematical Methods in The Applied Sciences, 198-209 (1987). https://onlinelibrary.wiley.com/doi/10.1002/mma.1670090115
  • Hackbusch, W., Multi-grid Methods and Applicatons, Springer, Berlin- HeidelBerg- New York, 1985. https://link.springer.com/book/10.1007/978-3-662-02427-0
  • Hackbusch, W., Mittelmann, H. D., On Multi-grid methods for variational inequalities, Numerische Mathematik, 42 (1983), 65-75 (1983). http://resolver.sub.unigoettingen.de/purl?PPN362160546 0042
  • Haiour, M., Etude de la convergence uniforme de la methode multigrilles appliquees aux problemes frontieres libres, PhD thesis, Universite de Annaba-Badji Mokhtar.https://www.pnst.cerist.dz/detail.php?id=19817/
  • Hoppe, R. H. W., Multi-grid methods for Hamilton-Jacobi-Bellman equations, Numerische Mathematik, 49(2) (1986), 239–254. https://link.springer.com/article/10.1007/BF01389627
  • Hoppe, R. H. W., Multigrid algorithms for variational inequalities, SIAM Journal on Numerical Analysis, 24(5) (1987), 1046–1065. https://www.jstor.org/stable/2157638
  • Kinderlehrer, D., Stampacchia, G., An Introduction to Variational Inequalities and their Applications, Academic Press, New York, 1980. https://lib.ugent.be/en/catalog/ebk01:1000000000551554
  • Nesba, N. E. H., Beggas, M., Belouafi, M. E., Ahmad, I., Ahmad, H., Askar, S., Multigrid methods for the solution of nonlinear variational inequalities, European Journal of Pure and Applied Mathematics Published by New York Business Global, 16(3) (2023), 1956-1969. https://ejpam.com/index.php/ejpam/article/view/4835
  • Reusken, A., Introduction to multigrid methods for elliptic boundary value problems, Inst, fur Geometrie und Praktische Mathematik, (2008). https://www.igpm.rwthaachen.de/Download/reports/reusken/ARpaper53.pdf
  • Reusken, A., On maximum norm convergcnce of multigrids methods for elliptic boundary value problems, SIAM J. Numer. Anal, 29(6) (1992), 1569-1578. https://epubs.siam.org/doi/abs/10.1137/0731020

Yıl 2024, Cilt: 73 Sayı: 1, 222 - 234, 16.03.2024

Nour El Houda Nesba Mohammed Beggas

https://doi.org/10.31801/cfsuasmas.1225525

Öz

Kaynakça

  • Boulbrachene, M., Haiour, M., The finite element approximation of Hamilton-Jacobi- Bellman equations, Computers & Mathematics with Applications, 41(7-8) (2001), 993–1007. https://www.sciencedirect.com/science/article/pii/S0898122100003345
  • Brezzi, F., Caffarelli, L. A., Convergence of the discrete free boundary for finite element approximations, R.A.I.R.O Anal. Numer., 17 (1983), 385-395. https://eudml.org/doc/193422
  • Ciarlet, P-G., Raviart, P-A., Maximum principle and uniform convergence for the finite element method, Computer Methods in Applied Mechanics and Engineering, 2(1) (1973), 17–31. https://doi.org/10.1016/0045-7825(73)90019-4
  • Cortey-Dumont, P., On the finite element approximation in the $L^{\infty}$ norm of variational inequalities with nonlinear operators, Numer.Num., 47 (1985), 45-57. https://eudml.org/doc/133022
  • Cortey-Dumont, P., Sur I’analyse num´erique des equations de Hamilton-Jacobi-Bellman, Mathematical Methods in The Applied Sciences, 198-209 (1987). https://onlinelibrary.wiley.com/doi/10.1002/mma.1670090115
  • Hackbusch, W., Multi-grid Methods and Applicatons, Springer, Berlin- HeidelBerg- New York, 1985. https://link.springer.com/book/10.1007/978-3-662-02427-0
  • Hackbusch, W., Mittelmann, H. D., On Multi-grid methods for variational inequalities, Numerische Mathematik, 42 (1983), 65-75 (1983). http://resolver.sub.unigoettingen.de/purl?PPN362160546 0042
  • Haiour, M., Etude de la convergence uniforme de la methode multigrilles appliquees aux problemes frontieres libres, PhD thesis, Universite de Annaba-Badji Mokhtar.https://www.pnst.cerist.dz/detail.php?id=19817/
  • Hoppe, R. H. W., Multi-grid methods for Hamilton-Jacobi-Bellman equations, Numerische Mathematik, 49(2) (1986), 239–254. https://link.springer.com/article/10.1007/BF01389627
  • Hoppe, R. H. W., Multigrid algorithms for variational inequalities, SIAM Journal on Numerical Analysis, 24(5) (1987), 1046–1065. https://www.jstor.org/stable/2157638
  • Kinderlehrer, D., Stampacchia, G., An Introduction to Variational Inequalities and their Applications, Academic Press, New York, 1980. https://lib.ugent.be/en/catalog/ebk01:1000000000551554
  • Nesba, N. E. H., Beggas, M., Belouafi, M. E., Ahmad, I., Ahmad, H., Askar, S., Multigrid methods for the solution of nonlinear variational inequalities, European Journal of Pure and Applied Mathematics Published by New York Business Global, 16(3) (2023), 1956-1969. https://ejpam.com/index.php/ejpam/article/view/4835
  • Reusken, A., Introduction to multigrid methods for elliptic boundary value problems, Inst, fur Geometrie und Praktische Mathematik, (2008). https://www.igpm.rwthaachen.de/Download/reports/reusken/ARpaper53.pdf
  • Reusken, A., On maximum norm convergcnce of multigrids methods for elliptic boundary value problems, SIAM J. Numer. Anal, 29(6) (1992), 1569-1578. https://epubs.siam.org/doi/abs/10.1137/0731020
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik
Bölüm Research Article
Yazarlar

Nour El Houda Nesba 0000-0003-0800-8253

Mohammed Beggas 0000-0002-7926-7802

Yayımlanma Tarihi 16 Mart 2024
Gönderilme Tarihi 28 Aralık 2022
Kabul Tarihi 2 Kasım 2023
Yayımlandığı Sayı Yıl 2024 Cilt: 73 Sayı: 1

Kaynak Göster

APA Nesba, N. E. H., & Beggas, M. (2024). Multigrid methods for non coercive variational inequalities. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 73(1), 222-234. https://doi.org/10.31801/cfsuasmas.1225525
AMA Nesba NEH, Beggas M. Multigrid methods for non coercive variational inequalities. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Mart 2024;73(1):222-234. doi:10.31801/cfsuasmas.1225525
Chicago Nesba, Nour El Houda, ve Mohammed Beggas. “Multigrid Methods for Non Coercive Variational Inequalities”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73, sy. 1 (Mart 2024): 222-34. https://doi.org/10.31801/cfsuasmas.1225525.
EndNote Nesba NEH, Beggas M (01 Mart 2024) Multigrid methods for non coercive variational inequalities. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73 1 222–234.
IEEE N. E. H. Nesba ve M. Beggas, “Multigrid methods for non coercive variational inequalities”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 73, sy. 1, ss. 222–234, 2024, doi: 10.31801/cfsuasmas.1225525.
ISNAD Nesba, Nour El Houda - Beggas, Mohammed. “Multigrid Methods for Non Coercive Variational Inequalities”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73/1 (Mart 2024), 222-234. https://doi.org/10.31801/cfsuasmas.1225525.
JAMA Nesba NEH, Beggas M. Multigrid methods for non coercive variational inequalities. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2024;73:222–234.
MLA Nesba, Nour El Houda ve Mohammed Beggas. “Multigrid Methods for Non Coercive Variational Inequalities”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 73, sy. 1, 2024, ss. 222-34, doi:10.31801/cfsuasmas.1225525.
Vancouver Nesba NEH, Beggas M. Multigrid methods for non coercive variational inequalities. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2024;73(1):222-34.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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