On the aposteriori error estimates for finite‐element solutions

Abstract

The analysis of the accuracy of the aposteriori error estimation procedure for finite‐element solutions is presented. The function Y — y is used as an aposteriori error estimator, here y ∈ S ₀ ^1,Δ is the finite‐element solution of the given problem and Y ∈ S ₀ ^2,Δis the high order solution of the same problem. The second order accuracy is proved for this error estimator in the L ₂, H ₁ and L₈ norms. Results of numerical experiments are presented.