Mimetic Discretizations with B-Splines

On the Construction of a Discrete Hodge Star Operator

Master thesis (2013)

Authors

G.L. Kooij Aerospace Engineering

Contributors

Hester Bijl Aerospace Engineering (mentor)
M.I. Gerritsma Aerodynamics (mentor)
Faculty
Aerospace Engineering, Aerospace Engineering
Copyright: © 2013 Gijs Kooij
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Published Date

21-02-2013

Language

English

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Faculty

Aerospace Engineering

Abstract

This thesis introduces a higher-order numerical method for elliptic boundary value problems. The discretization method belongs to the class of mimetic discretizations, which translate as many of properties of the continuous problem to the discrete system, aiming to improve accuracy and reliability. The novelty lies in the application of B-splines as basis functions in a dual grid approach. B-splines or basis splines are piecewise polynomials with a certain degree of continuity between the polynomial pieces. Therefore, splines offer an attractive compromise between piecewise linear functions, commonly seen in finite element analysis, and the Lagrange polynomials from spectral element methods.

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