Preconditioning Higher Order Finite Element Systems by Algebraic Multigrid Method of Linear Elements (Journal of Computational Mathematics, 2006)
We present and analyze a robust preconditioned conjugate gradient method for the higher order Lagrangian finite element systems of a class of elliptic problems. An auxiliary linear element stiffness matrix is chosen to be the preconditioner for higher order finite elements. Then an algebraic multigrid method of linear finite element is applied for solving the preconditioner. The optimal condition number which is independent of the mesh size is obtained. Numerical experiments confirm the efficiency of the algorithm.
Keywords: Finite element; Algebraic multigrid methods; Preconditioned Conjugate Gradient; Condition number.