Local (Commuting) THB-spline Projector

Master thesis (2022)

Authors

K.W. Dijkstra Electrical Engineering, Mathematics and Computer Science

Contributors

D. Toshniwal Numerical Analysis - EEMCS (supervisor 1)
Cornelis Vuik Delft Institute of Applied Mathematics (supervisor 2)
P.M. Visser Mathematical Physics - EEMCS (supervisor 2)
Faculty
Electrical Engineering, Mathematics and Computer Science
Copyright: © 2022 Kevin Dijkstra
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Published Date

30-11-2022

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

Existence of commuting THB-spline projectors is of importance in the field of numerical mathematics. These projectors are required to show that numerical solutions to the abstract Hodge Laplace problem are stable and consistent. We have introduced a local THB-spline projector based on Bezier projection, that commutes in the one-dimensional case. Additionally, to show that the projector is well posed in the univariate and multivariate case, we have derived so called projection elements, that are grouped mesh elements, on which the THB-splines are linearly independent.