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 Rd 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 Bh of B is formulated and optimal order error estimates are derived. Implementation issues are also discussed.