International Conference
"Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

Мосолапов А.О.   Rukavishnikov V.A.  

A new numerical method for solving Maxwell equations with strong singularity

Reporter: Rukavishnikov V.A.

In the present paper we develop the weighted edge finite element method (FEM) based on the conception of R-generalized solution of the Maxwell equations with strong singularity due to a reentrant corner on the boundary (see [1–3]). Numerical experiments of model problems showed that the rate of convergence of the numerical solution to the exact one is more than one and a half times better in comparison with the results established in [4–6]. Another advantage of this method is simplicity of the solution determination which is an additional benefit for numerical experiments.

This work was supported by Russian Foundation of Basic Research (grant 10-01-00060) and by Presidium of Far Eastern Branch of Russ. Acad. Sci. (project 09-II-SB-01-001).

1. Rukavishnikov V.A. Sov. Math., Dokl. 40 (1990). P. 653–655
2. Rukavishnikov V.A. Russ. J. Numer. Anal. Math. Model. 24 (2009) P. 565–590
3. Rukavishnikov V.A. and Rukavishnikova H.I. J. Comput. Appl. Math. 234 (2010) P. 2870–2882
4. Assous F., Ciarlet P., Garcia E. and Segré J. Comput. Methods in Appl. Mech. Engrg. 196 (2006) P. 665–681
5. Costabel M. and Daug M. Numer. Math. 93 (2002) P. 239–277
6. Jamelot E. C. R. Acad. Sci. Paris, Ser. I. 339 (2004) P. 809–814