@article{,
    author = {Apel, Thomas; Zilk, Philipp},
    title = {Isogeometric analysis of the Laplace eigenvalue problem on circular sectors: Regularity properties and graded meshes},
    editor = {},
    booktitle = {},
    series = {},
    journal = {Computers and Mathematics with Applications},
    address = {},
    publisher = {},
    edition = {},
    year = {2024},
    isbn = {},
    volume = {175},
    number =  {Special Issue on Mathematics of Scientific Computing for PDEs : recent advances on the occasion of Gundolf Haase's 60th birthday; Edited by Martin J. Gander, Fleurianne Bertrand, David Keyes, Barbara Kaltenbacher},
    pages = {236-254},
    url = {},
    doi = {10.1016/j.camwa.2024.09.018},
    keywords = {Isogeometric analysis ; Eigenvalue problems ; Corner singularities ; Graded mesh refinement ; Singular parameterizations ; Circular sectors},
    abstract = {The Laplace eigenvalue problem on circular sectors has eigenfunctions with corner singularities. Standard methods may produce suboptimal approximation results. To address this issue, a novel numerical algorithm that enhances standard isogeometric analysis is proposed in this paper by using a single-patch graded mesh refinement scheme. Numerical tests demonstrate optimal convergence rates for both the eigenvalues and eigenfunctions. Furthermore, the results show that smooth splines possess a superior approximation constant compared to their $C^0$-continuous counterparts for the lower part of the Laplace spectrum. This is an extension of previous findings about excellent spectral approximation properties of smooth splines on rectangular domains to circular sectors. In addition, graded meshes prove to be particularly advantageous for an accurate approximation of a limited number of eigenvalues. Finally, a hierarchical mesh structure is presented to avoid anisotropic elements in the physical domain and to omit redundant degrees of freedom in the vicinity of the singularity. Numerical results validate the effectiveness of hierarchical mesh grading for simulating eigenfunctions of low and high regularity.},
    note = {},
    institution = {Universität der Bundeswehr München, Fakultät für Bauingenieurwesen und Umweltwissenschaften, BAU 1 - Institut für Mathematik und Computergestützte Simulation, Professur: Apel, Thomas},
    
    
}