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math.NA2025
Error Estimates and Graded Mesh Refinement for Isogeometric Analysis on Polar Domains with Corners
Thomas Apel, Philipp Zilk
Isogeometric analysis (IGA) enables exact representations of computational geometries and higher-order approximation of PDEs. In non-smooth domains, however, singularities near cor…
math.NA2024
Isogeometric analysis of the Laplace eigenvalue problem on circular sectors: Regularity properties, graded meshes & variational crimes
Thomas Apel, Philipp Zilk
The Laplace eigenvalue problem on circular sectors has eigenfunctions with corner singularities. Standard methods may produce suboptimal approximation results. To address this issu…