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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/1325926
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