Finite Element Error Estimates for a Blast Furnace Gas Flow Problem

In the mathematical modeling of gas flow in an iron-making blast furnace, a nonlinear second-order boundary value problem is obtained. The operator associated with this problem is monotone and continuous. This paper shows how the algebraic properties of the principal nonlinear coefficient may be exploited to derive optimal order energy error estimates for the finite element approximations of this problem. The situation where the coefficient is implicitly defined is also considered.