Verification of functional a posteriori error estimates for obstacle problem in 1D
This work provides a verification of error estimates for a specific class of variational inequalities, but is limited to 1D and is incremental.
The authors verify a functional a posteriori error estimate for the obstacle problem in 1D by constructing a nonlinear benchmark with an exact solution, showing that the majorant error estimate bounds the finite element approximation error from above.
We verify functional a posteriori error estimate for obstacle problem proposed by Repin. Simplification into 1D allows for the construction of a nonlinear benchmark for which an exact solution of the obstacle problem can be derived. Quality of a numerical approximation obtained by the finite element method is compared with the exact solution and the error of approximation is bounded from above by a majorant error estimate. The sharpness of the majorant error estimate is discussed.