Finite element methods for nonlinear elliptic systems of second order

This paper deals with the finite element displacement method for approximating isolated solutions of general quasilinear elliptic systems. Under minimal assumptions on the structure of the continuous problems it is shown that the discrete analogues also have locally unique solutions which converge with quasi‐optimal rates in L2 and L∞. The essential tools of the proof are a deformation argument and a technique using weighted L2‐norms.