An Efficient Spectral Method for Second-Order Elliptic Equations with Variable Coefficients on a Planar Circular Sector

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Spectral method solves elliptic equations in a circular sector, indicating effective numerical convergence.

The proposed spectral method achieves effective results for solving elliptic equations with variable coefficients.
Numerical experiments confirmed that the algorithm demonstrates convergence on a standard rectangular domain.
The method utilizes a weak formulation constructed in weighted Sobolev spaces based on the Lax-Milgram lemma.
This approach is significant for numerical solutions in complex geometries like planar circular sectors.

Zhu et al. (2025) studied this question.

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