Rate of convergence of attractors for the discretization of differential equations of parabolic type using the method of finite elements

• Grant number: 09/08435-0
• Support Opportunities: Regular Research Grants
• Start date: September 01, 2009
• End date: August 31, 2011
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: German Jesus Lozada Cruz
• Grantee: German Jesus Lozada Cruz
• 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 study the approximation of semilinear parabolic equations through its discretization using the finite element method. We prove that the attractors of discretization they behave continuously when the step size tends to zero extending the results of Bruschi-Carvalho-Ruas-Filho (JDE 2000). We will also study the rate of convergence of the attractors in terms of the discretization step (AU)

Scientific publications

(9)

(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, 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)

ARAGAO-COSTA, E. R.; FIGUEROA-LOPEZ, R. N.; LANGA, J. A.; LOZADA-CRUZ, G.. Topological Structural Stability of Partial Differential Equations on Projected Spaces. Journal of Dynamics and Differential Equations, v. 30, n. 2, p. 687-718, JUN 2018. (14/02899-3, 15/24095-6, 14/19915-1, 13/21155-2, 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)

CARVALHO, A. N.; CHOLEWA, J. W.; LOZADA-CRUZ, G.; PRIMO, M. R. T.. REDUCTION OF INFINITE DIMENSIONAL SYSTEMS TO FINITE DIMENSIONS: COMPACT CONVERGENCE APPROACH. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, v. 45, n. 2, p. 600-638, 2013. (09/52687-4, 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. 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)