In this paper we compare the approximation properties of degree p spline spaces with different numbers of continuous derivatives. We prove that, for a given space dimension, Cp-1 splines provide better a priori error bounds for the approximation of functions in Hp+1(0 , 1). Our result holds for all practically interesting cases when comparing Cp-1 splines with C- 1 (discontinuous) splines. When comparing Cp-1 splines with C splines our proof covers almost all cases for p≥ 3 , but we can not conclude anything for p= 2. The results are generalized to the approximation of functions in Hq+1(0 , 1) for q< p, to broken Sobolev spaces and to tensor product spaces.
Approximation in FEM, DG and IGA: a theoretical comparison
Bressan A.;
2019-01-01
Abstract
In this paper we compare the approximation properties of degree p spline spaces with different numbers of continuous derivatives. We prove that, for a given space dimension, Cp-1 splines provide better a priori error bounds for the approximation of functions in Hp+1(0 , 1). Our result holds for all practically interesting cases when comparing Cp-1 splines with C- 1 (discontinuous) splines. When comparing Cp-1 splines with C splines our proof covers almost all cases for p≥ 3 , but we can not conclude anything for p= 2. The results are generalized to the approximation of functions in Hq+1(0 , 1) for q< p, to broken Sobolev spaces and to tensor product spaces.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
