2018/06/12 by Quanling Deng, Vladimir Puzyrev, Deng, Quanling +3
Engineering · #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1806.04286
openalex publication_date 2018/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We approximate the spectra of a class of 2n-order differential operators using isogeometric analysis in mixed formulations. This class includes a wide range of differential operators such as those arising in elliptic, biharmonic, Cahn-Hilliard, Swift-Hohenberg, and phase-field crystal equations. The spectra of the differential operators are approximated by solving differential eigenvalue problems in mixed formulations, which require auxiliary parameters. The mixed isogeometric formulation when applying classical quadrature rules leads to an eigenvalue error convergence of order 2p where p is the order of the underlying B-spline space. We improve this order to be 2p+2 by applying optimally-blended quadrature rules developed in \cite20,52 and this order is an optimum in the view of dispersion error. We also compare these results with the mixed finite elements and show numerically that mixed isogeometric analysis leads to significantly better spectral approximations.