A high-accuracy post-processing technique for free boundaries in finite element approximations to obstacle problems (Q1569341)

A suitable post-processing technique is combined with finite element approximations to obstacle problems. If the coincidence set is an interior starlike domain with analytical boundary \(F\), the author defines a discrete free boundary so that it can be easily computed and converges of distance \(h\) from \(F\) with the rate \(\varepsilon(h)\ln^3(1/h)\), \(\varepsilon(h)=h\|{u-u_h}\|_{H^1}+\|u-u_h\|_{L_2}\). Here \(H^1, L_2\) are the classical Hilbert spaces.