Higher order Fourier finite element methods for Hodge Laplacian problems on axisymmetric domains

Author

Nicole E. Stock, James Madison UniversityFollow

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.

Date of Graduation

5-9-2021

Publish

yes

Document Type

Thesis

Degree Name

Bachelor of Science (BS)

Department

Department of Mathematics and Statistics

Advisor(s)

Minah Oh

Stephen Lucas

Roger Thelwell

Abstract

We construct efficient higher order Fourier finite element spaces to approximate the solution of Hodge Laplacian problems on axisymmetric domains. In [16], a new family of Fourier finite element spaces was constructed by using the lowest order finite element methods. These spaces were used to discretize Hodge Laplacian problems in [18]. In this research, we extend the results of [16,18] by constructing higher order Fourier finite element spaces. We demonstrate that these new higher order Fourier finite element methods provide improved computational efficiency as well as increased accuracy.

Recommended Citation

Stock, Nicole E., "Higher order Fourier finite element methods for Hodge Laplacian problems on axisymmetric domains" (2021). Senior Honors Projects, 2020-current. 131.
https://commons.lib.jmu.edu/honors202029/131