A Nonoverlapping Domain Decomposition Preconditioner for a Symmetric Interior Penalty Method

In this talk we will discuss a nonoverlapping domain decomposition pre-conditioner for the symmetric interior penalty Galerkin method [1, 2, 3]. Thepreconditioner is based on balancing domain decomposition by constraints [4].Theoretical results on the condition number estimate of the preconditioned sys-tem will be presented along with numerical results. References[1] J. Douglas, Jr. and T. Dupont. Interior penalty procedures for elliptic andparabolic Galerkin methods. Lecture Notes in Phys. 58, Springer-Verlag,Berlin, 1976.[2] M.F. Wheeler. An elliptic collocation-finite-element method with interiorpenalties. SIAM J. Numer. Anal., 15:152–161, 1978.[3] D.N. Arnold. An interior penalty finite element method with discontinuouselements. SIAM J. Numer. Anal., 19:742–760, 1982.[4] C.R. Dohrmann. A preconditioner for substructuring based on constrainedenergy minimization. SIAM J. Sci. Comput., 25:246–258, 2003.