American Institute of Mathematical Sciences

Advanced
February  2001, 1(1): 71-88. doi: 10.3934/dcdsb.2001.1.71

On the box method for a non-local parabolic variational inequality

Walter Allegretto 1, , Yanping Lin 2, and  Shuqing Ma 1,

1. 

Department of Mathematical Sciences, University of Alberta, Edmonton A B, Canada T6G 2G1
2. 

Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1, Canada

Received  September 2000 Revised  November 2000 Published  January 2001

In this paper we study a box scheme (or finite volume element method) for a non-local nonlinear parabolic variational inequality arising in the study of thermistor problems. Under some assumptions on the data and regularity of the solution, optimal error estimates in the $H^1$-norm are attained.
Keywords: Box methods, non-local, thermistor and variational inequality..
Mathematics Subject Classification: 76S0.
Citation: Walter Allegretto, Yanping Lin, Shuqing Ma. On the box method for a non-local parabolic variational inequality. Discrete & Continuous Dynamical Systems - B, 2001, 1 (1) : 71-88. doi: 10.3934/dcdsb.2001.1.71
[1]

Raffaella Servadei, Enrico Valdinoci. Variational methods for non-local operators of elliptic type. Discrete & Continuous Dynamical Systems, 2013, 33 (5) : 2105-2137. doi: 10.3934/dcds.2013.33.2105
[2]

Shixiu Zheng, Zhilei Xu, Huan Yang, Jintao Song, Zhenkuan Pan. Comparisons of different methods for balanced data classification under the discrete non-local total variational framework. Mathematical Foundations of Computing, 2019, 2 (1) : 11-28. doi: 10.3934/mfc.2019002
[3]

Christos V. Nikolopoulos, Georgios E. Zouraris. Numerical solution of a non-local elliptic problem modeling a thermistor with a finite element and a finite volume method. Conference Publications, 2007, 2007 (Special) : 768-778. doi: 10.3934/proc.2007.2007.768
[4]

Anouar Bahrouni. Trudinger-Moser type inequality and existence of solution for perturbed non-local elliptic operators with exponential nonlinearity. Communications on Pure & Applied Analysis, 2017, 16 (1) : 243-252. doi: 10.3934/cpaa.2017011
[5]

Li Wang, Yang Li, Liwei Zhang. A differential equation method for solving box constrained variational inequality problems. Journal of Industrial & Management Optimization, 2011, 7 (1) : 183-198. doi: 10.3934/jimo.2011.7.183
[6]

Qiyu Jin, Ion Grama, Quansheng Liu. Convergence theorems for the Non-Local Means filter. Inverse Problems & Imaging, 2018, 12 (4) : 853-881. doi: 10.3934/ipi.2018036
[7]

Gabriel Peyré, Sébastien Bougleux, Laurent Cohen. Non-local regularization of inverse problems. Inverse Problems & Imaging, 2011, 5 (2) : 511-530. doi: 10.3934/ipi.2011.5.511
[8]

Olivier Bonnefon, Jérôme Coville, Guillaume Legendre. Concentration phenomenon in some non-local equation. Discrete & Continuous Dynamical Systems - B, 2017, 22 (3) : 763-781. doi: 10.3934/dcdsb.2017037
[9]

Henri Berestycki, Nancy Rodríguez. A non-local bistable reaction-diffusion equation with a gap. Discrete & Continuous Dynamical Systems, 2017, 37 (2) : 685-723. doi: 10.3934/dcds.2017029
[10]

Matteo Focardi. Vector-valued obstacle problems for non-local energies. Discrete & Continuous Dynamical Systems - B, 2012, 17 (2) : 487-507. doi: 10.3934/dcdsb.2012.17.487
[11]

Chiu-Yen Kao, Yuan Lou, Wenxian Shen. Random dispersal vs. non-local dispersal. Discrete & Continuous Dynamical Systems, 2010, 26 (2) : 551-596. doi: 10.3934/dcds.2010.26.551
[12]

Hongjie Dong, Doyoon Kim. Schauder estimates for a class of non-local elliptic equations. Discrete & Continuous Dynamical Systems, 2013, 33 (6) : 2319-2347. doi: 10.3934/dcds.2013.33.2319
[13]

Tao Wang. Global dynamics of a non-local delayed differential equation in the half plane. Communications on Pure & Applied Analysis, 2014, 13 (6) : 2475-2492. doi: 10.3934/cpaa.2014.13.2475
[14]

Florent Berthelin, Paola Goatin. Regularity results for the solutions of a non-local model of traffic flow. Discrete & Continuous Dynamical Systems, 2019, 39 (6) : 3197-3213. doi: 10.3934/dcds.2019132
[15]

Jared C. Bronski, Razvan C. Fetecau, Thomas N. Gambill. A note on a non-local Kuramoto-Sivashinsky equation. Discrete & Continuous Dynamical Systems, 2007, 18 (4) : 701-707. doi: 10.3934/dcds.2007.18.701
[16]

Antonio Greco, Vincenzino Mascia. Non-local sublinear problems: Existence, comparison, and radial symmetry. Discrete & Continuous Dynamical Systems, 2019, 39 (1) : 503-519. doi: 10.3934/dcds.2019021
[17]

Felisia Angela Chiarello, Paola Goatin. Non-local multi-class traffic flow models. Networks & Heterogeneous Media, 2019, 14 (2) : 371-387. doi: 10.3934/nhm.2019015
[18]

Niels Jacob, Feng-Yu Wang. Higher order eigenvalues for non-local Schrödinger operators. Communications on Pure & Applied Analysis, 2018, 17 (1) : 191-208. doi: 10.3934/cpaa.2018012
[19]

Rafael Abreu, Cristian Morales-Rodrigo, Antonio Suárez. Some eigenvalue problems with non-local boundary conditions and applications. Communications on Pure & Applied Analysis, 2014, 13 (6) : 2465-2474. doi: 10.3934/cpaa.2014.13.2465
[20]

Yuanhong Wei, Xifeng Su. On a class of non-local elliptic equations with asymptotically linear term. Discrete & Continuous Dynamical Systems, 2018, 38 (12) : 6287-6304. doi: 10.3934/dcds.2018154

2020 Impact Factor: 1.327

Tools

Metrics

  • PDF downloads (60)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy