Continuity of attractors for the discretization of parabolic problems using finite element method

• Grant number: 09/08088-9
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: August 01, 2009
• End date: July 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: German Jesus Lozada Cruz
• Grantee: Rodiak Nicolai Figueroa López
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil

Abstract

In this project we will study the approximations of semilinear parabolic equations through its discretization using finite element method. We will prove the continuity of the attractors when step size of the discretization tends to zero extending the results of Bruschi-Carvalho-Ruas-Filho (JDE 2000). Also we will study the rate of convergence of the attractors in terms of the discretization step.

Scientific publications

(7)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

FIGUEROA-LOPEZ, RODIAK; LOZADA-CRUZ, GERMAN. On Global Attractors for a Class of Parabolic Problems. APPLIED MATHEMATICS & INFORMATION SCIENCES, v. 8, n. 2, p. 8-pg., 2014-03-01. (09/08088-9, 09/08435-0)

FIGUEROA-LOPEZ, R.; LOZADA-CRUZ, G.. A SEMIGROUPS THEORY APPROACH TO A MODEL OF SUSPENSION BRIDGES. Electronic Journal of Qualitative Theory of Differential Equations, v. N/A, n. 51, p. 10-pg., 2013-01-01. (09/08088-9, 09/08435-0)

FIGUEROA-LOPEZ, R.; LOZADA-CRUZ, G.. Some estimates for resolvent operators under the discretization by finite element method. COMPUTATIONAL & APPLIED MATHEMATICS, v. 34, n. 3, p. 1105-1116, OCT 2015. (09/08088-9, 09/08435-0)

FIGUEROA-LOPEZ, R.; LOZADA-CRUZ, G.. A SEMIGROUPS THEORY APPROACH TO A MODEL OF SUSPENSION BRIDGES. Electronic Journal of Qualitative Theory of Differential Equations, n. 51, p. 1-10, 2013. (09/08088-9, 09/08435-0)

FIGUEROA-LOPEZ, RODIAK; LOZADA-CRUZ, GERMAN. On Global Attractors for a Class of Parabolic Problems. APPLIED MATHEMATICS & INFORMATION SCIENCES, v. 8, n. 2, p. 493-500, MAR 2014. (09/08088-9, 09/08435-0)

FIGUEROA-LOPEZ, R. N.; LOZADA-CRUZ, G.. Dynamics of parabolic equations via the finite element method I. Continuity of the set of equilibria. Journal of Differential Equations, v. 261, n. 9, p. 5235-5259, NOV 5 2016. (09/08088-9, 09/08435-0, 13/21155-2)

FIGUEROA-LOPEZ, R.; LOZADA-CRUZ, G.. Some estimates for resolvent operators under the discretization by finite element method. COMPUTATIONAL & APPLIED MATHEMATICS, v. 34, n. 3, p. 12-pg., 2015-10-01. (09/08088-9, 09/08435-0)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

LÓPEZ, Rodiak Nicolai Figueroa. Continuidade de atratores para a discretização de problemas parabólicos usando o método de elementos finitos. 2013. Doctoral Thesis - Universidade Estadual Paulista (Unesp). Instituto de Biociências Letras e Ciências Exatas. São José do Rio Preto São José do Rio Preto.