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Date of Graduation
Bachelor of Science (BS)
Department of Mathematics and Statistics
We construct efficient higher order Fourier finite element spaces to approximate the solution of Hodge Laplacian problems on axisymmetric domains. In , 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 . 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.
Stock, Nicole E., "Higher order Fourier finite element methods for Hodge Laplacian problems on axisymmetric domains" (2021). Senior Honors Projects, 2020-current. 131.