Journal article

Publication year: 2021

Pages: 250-272

Journal: Applied and Computational Harmonic Analysis

Volume number: 54

ISSN: 1063-5203

eISSN: 1096-603X

DOI Link: https://doi.org/10.1016/j.acha.2021.03.002

Publisher: Elsevier

Abstract: 
We present a construction of C-1 piecewise quadratic hierarchical bases of Lagrange type on arbitrary polygonal domains Omega subset of R-2. Properly normalized, these bases are Riesz bases for Sobolev spaces H-s (Omega), with s is an element of (1, 5/2). The method is applicable to arbitrary initial triangulations of polygonal domains, and does not require a checkerboard quadrangulation needed for earlier C-1 cubic hierarchical Lagrange bases. Homogeneous boundary conditions can be taken into account in a natural way, and lead to Riesz bases for Sobolev spaces H-0(s) (Omega), s is an element of(1, 5/2) \ {3/2}, and H-00(3/2) (Omega). (C) 2021 Elsevier Inc. All rights reserved.

Harvard Citation style: Davydov, O. and Yeo, W. (2021) C¹ piecewise quadratic hierarchical bases, Applied and Computational Harmonic Analysis, 54, pp. 250-272. https://doi.org/10.1016/j.acha.2021.03.002

APA Citation style: Davydov, O., & Yeo, W. (2021). C¹ piecewise quadratic hierarchical bases. Applied and Computational Harmonic Analysis. 54, 250-272. https://doi.org/10.1016/j.acha.2021.03.002