A Multigrid Algorithm Of The Rectangle Morley Element Method For Solving The Fourth Order Elliptic Problem

In this dissertation, we study a multigrid algorithm of the rect-angle Morley element method for solving the fourth order elliptic problem.First of all, we derise the variational form of the fourth order elliptic problem, and introduce the rectangle Morley element and the discrete approximation of the rectangle Morley element for the fourth order elliptic problem. Next, we devise an intergrid transfer opera-tor, and prove the stability and the approximative property of the intergrid transfer operator. Then, we propose a W-cycle multigrid algorithm, and prove the smoothness and the approximative prop-erty, and show the optimal convergence of W-cycle multigrid algo-rithm. Finally, numerical experiments are presented to conform our theoretical results.