An optimal order multigrid method for biharmonic,C1 finite element equations

Summary In this paper, we study a special multigrid method for solving large linear systems which arise from discretizing biharmonic problems by the Hsieh-Clough-Tocher,C¹ macro finite elements or several otherC¹ finite elements. Since the multipleC¹ finite element spaces considered are not nested, the nodal interpolation operator is used to transfer functions between consecutive levels in the multigrid method. This method converges with the optimal computational order.