Global Estimates for Mixed Methods for Second Order Elliptic Equations

Global error estimates in L²(Ω ), L^∞ (Ω ), and H- s(Ω ), Ω in R² or R³, are derived for a mixed finite element method for the Dirichlet problem for the elliptic operator Lp = - div(a\;grad\;p + bp) + cp based on the Raviart-Thomas-Nedelec space Vₕ × Wₕ ⊂ H(div;Ω ) × L²(Ω ) . Optimal order estimates are obtained for the approximation of p and the associated velocity field u = - (a\;grad\;p + bp) in L²(Ω ) and H- s(Ω ), 0 s k + 1, and, if Ω ⊂ R² for p in L^∞ (Ω ).