New publication in Computer Methods in Applied Mechanics and Engineering

7 Januar 2026

Our article “Error estimates and graded mesh refinement for isogeometric analysis in the vicinity of polar corners” has recently been published in the journal Computer Methods in Applied Mechanics and Engineering.

In this paper, we investigate isogeometric analysis on polar domains with corners, which frequently occur in CAD-based applications, for instance in rotationally symmetric geometries. Such parameterizations possess a singularity at the polar point, while the corner gives rise to a singularity in the PDE solution; neither effect is accounted for in classical IGA approximation theory.

To address this gap, we develop a numerical analysis tailored to polar geometries based on weighted Sobolev spaces and derive corresponding a priori error estimates. In addition, we propose and analyze a simple mesh grading scheme allowing local refinement towards the polar corner, showing that optimal convergence rates can be achieved in the presence of singular solutions. The theoretical results are supported by a series of illustrative examples and provide practical guidance for the effective treatment of corner singularities in isogeometric analysis.

Apel, T., Zilk, P. (2026): Error estimates and graded mesh refinement for isogeometric analysis in the vicinity of polar corners, Computer Methods in Applied Mechanics and Engineering, 452, 118695, DOI (Open Access)