On the error estimate of finite difference method for the obstacle problem (Q864787)

A 2D obstacle problem is considered. It is written as an elliptic variational inequality of the first kind: find \(u \in K\) such that \[ a(u,v-u)\geq(f,v-u) \quad\text{for any }v \in K, \] where \(K\) is, as usual, a closed convex subset of some Hilbert space \(V\), here of \(V=H^1_0 (\Omega)\), with \(\Omega\) a 2D domain. The corresponding differential operator is \(-\Delta\). The maximum principle is applied for two mesh sets and the error estimates are derived. The finite difference schemes are the 5-point second order and the 9-point compact fourth-order one. Numerical results and graphics are presented.