Verification of functional a posteriori error estimates for an obstacle problem

Abstract

We verify functional a posteriori error estimate proposed by S. Repin for an obstacle problem. A new benchmark with known analytical solution in 2D is constructed. Numerical approximation is obtained by the finite element method using bilinear elements on a rectangular mesh. Error of the approximation is measured in the energy norm and bounded from above by a functional majorant. Numerical tests provide sharp quality of the studied error estimate.