A least-squares finite element method for solving the polygonal-line arc-scattering problem

Abstract

This paper is concerned with the scattering problem of a polygonal-line arc. We solve this polygonal-line arc-scattering problem by a least-squares finite element method. In the method, Fourier–Bessel functions is used to capture the singularities around tips and corners. A combination of fundamental solutions is used to represent the scattered field towards infinity. We also analyse the convergence and give an error estimate of the method. Numerical experiments are also presented to show the effectiveness of our method.

Keywords:

• arc scattering problem
• Helmholtz equation
• non-polynomial finite element method

AMS Subject Classifications:

• 65N30
• 65N80

Acknowledgments

The authors would like to thank the reviewers for their careful reading and valuable comments which led to the improvement of the quality of our submitted manuscript. The work was supported by the Fundamental Research Funds for the Central Universities under contract No.3132013332.