On a numerical method for solving obstacle problems (Q1330676)

The authors try to adapt a Fourier method for minimization of a coercive quadratic functional on a Hilbert space to solve a one-dimensional elliptic problem with an obstacle inside the one-dimensional domain. The problem in its classical formulation (see (4.1)--(4.2) in the paper) is expressed as a variational inequality (see (4.3)--(4.4)) which is eventually transformed to a linear system of equations (4.7). Nevertheless, neither of these three formulations seems to be equivalent with any other. Indeed, the classical formulation which misses the complementarity condition cannot be equivalent with the standard variational-inequality formulation. Both these formulations admit in the special case considered in the paper the trivial solution \(u=0\), which does not satisfy the third formulation (4.7), however. The paper also contains a lot of others discrepancies. As a result, the paper seems to be a bit out of usage.