Discontinuous Galerkin Finite Element Analysis of a Thermal coupling problem


  • Eduardo Lima de Oliveira
  • Silvia Cristina Belo e Silva
  • Héctor Vargas Poblete
  • Jiang Zhu
  • Abimael Fernando Loula




Raviart-Thomas methods, Discontinuous Galerkin nite element, elliptical nonlinear problem, mixed methods


In this work we use mixed formulations, based on the Raviart-Thomas (RTH) methods, considering the weak ow form between the elements of the nite element mesh. The thermal problem analyzed is an elliptical nonlinear problem. We propose a analysis, of model, considering the two elliptic coupled equations, in the mixed form and show numerical results which conrmoptimal convergence rates for the ows in H(div; Ω) and scalar variables in L2 (Ω).


Não há dados estatísticos.

Biografia do Autor

Eduardo Lima de Oliveira

UEA, Manaus, AM

Silvia Cristina Belo e Silva

UEA, Manaus, AM

Héctor Vargas Poblete

LNCC, Petrópolis, RJ

Jiang Zhu

LNCC, Petrópolis, RJ

Abimael Fernando Loula

LNCC, Petrópolis, RJ


F. Brezzi and M. Fortin. Mixed and hybrid nite element methods. 1a. ed. New York: Springer-Verlang, 2012. doi: 10.1007/978-1-4612-3172-1.

P. G. Ciarlet. The nite element method for elliptic problems. 1a edition. Philadelphia: SIAM - Society for industrial and Applied Mathematics, 2002. isbn: 978-0-89871-514-9.

A. F. D. Loula and J. Zhu. Finite element analysis of a coupled nonlinear system. In: Computation and Applied Mathematics 34 (2001), pp. 321339. issn: 0101 - 8205.

N. G. Meyers. An L p -estimate for the gradient of solutions of second order elliptic divergence equations. In: Annali della Scuola Normale Superiore di Pisa 3 (1963), pp. 189206. issn: 0391-173X.

P.A. Raviart and J.M. Thomas. A mixed nite element method for 2-nd order elliptic problems. In: Mathematical Aspects of Finite Element Methods. Ed. by I. Galligani and E. Magenes. Vol. 606. Lecture Notes in Mathematics. Springer, 2006. Chap. 4, pp. 292315. doi: 10.1007/BFb0064470.

J. Zhu and A. F. D Loula. Mixed nite element analysis of a thermally nonlinear coupled problem. In: Numerical Methods for Partial Diferential Equations 1 (2006), pp. 180 196. doi: 10.1002/num.20093






Trabalhos Completos