Connection between finite volume and mixed finite element methods for a diffusion problem with nonconstant coefficients. Application to a convection diffusion problem. (English) Zbl 0839.65116

Agouzal, A.; Baranger, J.; Maitre, J.-F.; Oudin, F.

East-West J. Numer. Math. 3, No. 4, 237-254 (1995).

In a forthcoming paper, the authors have shown that the mixed finite element method based on the first Raviart-Thomas element combined with a suitable numerical integration formula yields a cell-centered finite volume scheme. Analogously, the authors study here the diffusion equations with nonconstant coefficients and apply the results to convection diffusion equations arising in semiconductor theory. Error bounds are also obtained. These results are applied to semiconductor problems, using the exponential fitting method described by F. Brezzi, L. D. Marini and P. Pietra [SIAM J. Numer. Anal. 26, No. 6, 1342-1355 (1989; Zbl 0686.65088)].

Reviewer: H.P.Dikshit (Jabalpur)

MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15	Error bounds for boundary value problems involving PDEs
35J25	Boundary value problems for second-order elliptic equations
78A55	Technical applications of optics and electromagnetic theory
35Q60	PDEs in connection with optics and electromagnetic theory

Keywords:

error bounds; mixed finite element method; Raviart-Thomas element; cell-centered finite volume scheme; diffusion equation; convection diffusion equation; semiconductor; exponential fitting method

Citations:

Zbl 0686.65088