Abstract
Abstract In this paper, we propose an H ( curl 2 ) \boldsymbol{H}(\mathbf{curl}^{2}) -conforming spectral elements to solve the quad-curl problem on cubic meshes in three dimensions. Starting with generalized vectorial Jacobi polynomials, we first construct the basis functions of the H ( curl 2 ) \boldsymbol{H}(\mathbf{curl}^{2}) -conforming spectral elements using the contravariant transform together with the affine mapping from the reference cube onto each physical element. Falling into four categories, interior modes, face modes, edge modes, and vertex modes, these H ( curl 2 ) \boldsymbol{H}(\mathbf{curl}^{2}) -conforming basis functions are constructed in an arbitrarily high degree with a hierarchical structure. Next, H ( curl 2 ) \boldsymbol{H}(\mathbf{curl}^{2}) -conforming spectral element approximation schemes are established to solve the boundary value problem as well as the eigenvalue problem of quad-curl equations. Numerical experiments demonstrate the effectiveness and efficiency of the ℎ-version and the 𝑝-version of our H ( curl 2 ) \boldsymbol{H}(\mathbf{curl}^{2}) -conforming spectral element method.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.