Discretization Methods for the Diffusion Equation

S. Van Criekingen

Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3111, U.S.A.

R. Beauwens
E.E. Lewis


Abstract

The diffusion equation arising from neutronics is an elliptic partial differential equation of the form -div(p grad u) + c u = f. Continuous second order, second order hybrid, mixed and mixed-hybrid formulations are investigated theoretically, each of them in a primal and dual version. A nodal finite element scheme is applied to the mixed-hybrid formulations. Well-posedness is investigated each time. A linear system is obtained, and early numerical results are provided.