High accuracy post-processing technique for free boundaries in finite element approximations to the obstacle problems

A suitable post-processing technique in combined with a finite element approximations to the obstacle problems. If the coincidence set is an interior star-like domain with analytical boundary $F$, we define discrete free boundary thus that it is easily computable and converges in distance to $F$ with a rate $\varepsilon(h)\ln^3(1/h)$, $\varepsilon(h)=h|u-u_k|_{H^1}+\|u-u_h\|_{L_2}$. Our present analysis does not rest on the discrete maximum principle.