On mixed error estimates for elliptic obstacle problems (Q5959279)

The authors describe the finite element approximation of the elliptic obstacle problem \[ \begin{cases}-\lim\text{div}(A\nabla u)\geq f, \\ u\geq \varphi, \\ (-\text{div}(A\nabla u)-f)(u-\varphi)=0, \end{cases} \] where \(A\) is a given matrix function, \(f\) and \(\varphi \) are given functions, and \(\Omega \) is a bounded open set in \({\mathbb R}^{2}.\) The authors derive sharp mixed error estimates for the problem with a zero obstacle. Both upper and lower bounds are established. The results are generalized to the case of a non-zero obstacle.