A mixed finite element method for boundary flux computation. (English) Zbl 0587.76143

Most finite element schemes for thermal problems estimate boundary heat flux directly from the derivative of the finite element solution. The boundary flux calculated by this approach is typically inaccurate and does not guarantee a global heat balance. In this paper we present a mixed finite element method for calculating the boundary flux and show the superiority of this method through numerical examples of both diffusion and advection-diffusion problems.


76R10 Free convection
Full Text: DOI


[1] Gresho, P. M.; Lee, R. L.: Don’t suppress the wiggles–they’re telling you something. Comput. & fluids 9, 223-253 (1981) · Zbl 0436.76065
[2] Carey, G. F.; Chow, S. S.; Seager, M. K.: Approximate boundary-flux calculations. Comput. meths. Appl. mech. Engrg. 50, 107-120 (1985) · Zbl 0546.73057
[3] Christie, I.; Griffiths, D. F.; Mitchell, A. R.; Zienkiewicz, O. C.: Finite element methods for second order differential equations with significant first derivatives. Internat. J. Numer. meths. Engrg. 10, 1389-1396 (1976) · Zbl 0342.65065
[4] Brooks, A. N.; Hughes, T. J. R.: Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. meths. Appl. mech. Engrg. 32, 199-259 (1982) · Zbl 0497.76041
[5] Hughes, T. J. R.; Brooks, A. N.: A theoretical framework for Petrov-Galerkin method with discontinuous weighting functions: application to the streamline upwind procedure. Finite elements in fluids 4 (1982)
[6] Wheeler, M. F.: A Galerkin procedure for estimating the flux for two-point boundary value problems. SIAM J. Numer. anal. 11, 764-768 (1974) · Zbl 0292.65046
[7] Carey, G. F.: Derivative calculation from finite element solutions. Comput. meths. Appl. mech. Engrg. 35, 1-14 (1982) · Zbl 0478.73052
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.