CM: Verification of functional a posteriori error estimates for a contact problem in 1D

Prof. Dr. Jan Valdman

Jan. 15, 2013, 2:30 p.m. S2 416

We verify functional a posteriori error estimates of numerical solutions of a contact problem in 1D. The contact problem is described by a quadratic minimization problem with a bound constrain and it can be equivalently formulated as a variational inequality. The simplification into 1D allows for the construction of a benchmark for which an exact solution can be derived. Numerical solution obtained by the finite element method can be compared with the exact solution and their difference is further estimated in the energetic norm by a functional majorant proposed by Repin et al. Numerical tests provide sharp estimation of the approximation error. This is a joint work with Petr Harasim (Ostrava).