Absolute Stable Homotopy Finite Element Methods for Circular Arch Problem and Asymptotic Exactness Posteriori Error Estimate (Journal of Computational Mathematics, 2021)
In this paper, HFEM is proposed to investigate the circular arch problem. Optimal error estimates are derived, some superconvergence results are established, and an asymptotic exactness posteriori error estimator is presented. In contrast with the classical displacement variational method, the optimal convergence rate for displacement is uniform to the small parameter. In contrast with classical mixed finite element methods, our results are free of the strict restriction on h (the mesh size) which is preserved by all the previous papers. Furtheremore, we introduce an asymptotic exactness posteriori error estimator based on a global superconvergence result which is discovered in this kind of problem for the first time.
Keywords: HFEM; arch; superconvergence; asymptotic exactness; posteriori error estimator.