Geodesic
High accuracy post-processing technique for free boundaries in finite element approximations to the obstacle problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 38 (1998) no. 2, pp. 239-246

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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. 
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     author = {R. Z. Dautov},
     title = {High accuracy post-processing technique for free boundaries in finite element approximations to the obstacle problems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {239--246},
     publisher = {mathdoc},
     volume = {38},
     number = {2},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1998_38_2_a6/}
}
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R. Z. Dautov. High accuracy post-processing technique for free boundaries in finite element approximations to the obstacle problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 38 (1998) no. 2, pp. 239-246. http://geodesic.mathdoc.fr/item/ZVMMF_1998_38_2_a6/