Optimal order error estimates for finite element approximations of a bifurcation function

The bifurcation function associated with an elliptic boundary value problem Au + g [ u ] = 0 is a vector field B ( ω ) on R d with the property that the solutions of the boundary value problem are in a one-to-one correspondence with the zeros of B. A finite element approximation B h of B is formulated and optimal order error estimates are derived. Implementation issues are also discussed.