In this paper, some enhanced error estimates are derived for the augmented subspace methods which designed solving eigenvalue problems. For first time, we strictly prove that have second order convergence rate between two iteration steps, is better than existing theoretical results in Lin and Xie (Math Comp 84:71–88, 2015), et al. (SIAM J Numer Anal 57(6):2519–2550, 2019), Xu Sci Comput 42(5):A...

This paper deals with a study the linear finite element approximation of piezoelectric Signorini's contact problem and without friction. We derive error estimates that depend on penalty parameter ε mesh size h. Moreover, under some regularities solution to problems requirements parameters h, we provide results convergence rate penalized solution.