A Two-Level Additive Schwarz Preconditioner for Local $C^0$ Discontinuous Galerkin Methods of Kirchhoff Plates

Abstract

A two-level additive Schwarz preconditioner based on the overlapping domain decomposition approach is proposed for the local $C^0$ discontinuous Galerkin (LCDG) method of Kirchhoff plates. Then with the help of an intergrid transfer operator and its error estimates, it is proved that the condition number is bounded by $O(1+(H^4/\delta ^4))$, where H is the diameter of the subdomains and $\delta $ measures the overlap among subdomains. And for some special cases of small overlap, the estimate can be improved as $O(1+(H^3/\delta ^3))$. At last, some numerical results are reported to demonstrate the high efficiency of the two-level additive Schwarz preconditioner.