Approximation in FEM, DG and IGA: A Theoretical Comparison

2018/08/13 by Bressan, Andrea, Sande, Espen · 6 citations
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1808.04163

Abstract

In this paper we compare approximation properties of degree p spline spaces with different numbers of continuous derivatives. We prove that, for a given space dimension, \smooth p-1 splines provide better a priori error bounds for the approximation of functions in H^p+1(0,1). Our result holds for all practically interesting cases when comparing \smooth p-1 splines with \smooth -1 (discontinuous) splines. When comparing \smooth p-1 splines with \smooth 0 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 H^q+1(0,1) for q

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