5 - Discretization Accuracy

Abstract

This chapter provides an overview of discretization accuracy and discusses how a choice of polynomials in shape functions becomes important in the light of an error analysis. According to Taylor's theorem, any analytic function is polynomial-like over a small interval. The chapter also illustrates error distribution in a displacement and the bending moment in a circular plate. The energy error depends not only on the number of elements but also on the location of the nodes. When some elements are halved without changing the location of the previous nodes, the total potential energy of the finer mesh cannot increase and convergence is monotonic. The chapter discusses the sharpness of the energy error estimate and explains the phenomenon of superconvergence. It also explains how the differential operators in boundary value problems are positive bounded. Knowledge of the theoretical rate of convergence can be used to improve the accuracy of the computed values through an extrapolation to h = 0.