A Two-level Additive Schwarz Preconditioning Algorithm For The Weak Galerkin Method Of The Second-order Elliptic Equation

In this dissertation, we study a two-level additive Schwarz precon-ditioning algorithm for the weak Galerkin method of the second-order elliptic equation.First of all, we briefly introduce the weak Galerkin finite element method and its error analysis for the second-order elliptic equation. Next, we propose a two-level additive Schwarz preconditioner and a intergrid transfer operator, and prove the stability and approximation of the intergrid transfer operator. Then we respectively estimate the maximal eigenvalue and the minimal eigenvalue of the preconditioned operator, and then obtain the upper bound of the condition number of the preconditioned operator. Finally, numerical experiments are presented to conform our theoretical results.