Convergence Analysis for Cubic Serendipity Finite Elements with Thirty-Two Degrees of Freedom
In this paper, we consider the Poisson problem with homogeneous Dirichlet boundary conditions on the bounded open domain and analyze convergence phenomena that appear by using cubic serendipity block elements with thirty-two degrees of freedom. By means of the standard Legendre polynomial technique, we derive an error estimate, which is not superconvergent and shows this serendipity element has not pointwise supercloseness properties.
J. H. Liu and X. C. Huo, "Convergence Analysis for Cubic Serendipity Finite Elements with Thirty-Two Degrees of Freedom", Advanced Materials Research, Vols. 268-270, pp. 501-504, 2011