An Algebraic Multigrid Method Of Quadratic Lagrangian Finite Element Equations Under The Unstructured Quadrilateral Grids

For an elliptic boundary problem with jump coefficients under the unstructured quadrilateral grid,we consider the algebraic multigrid(AMG) methods to solve the discretization systems of two kinds of Quadratic Lagrangian finite element equations(8-node quadrilateral finite element and 9-node quadrilateral finite element), by analyzing the algebraic relationship between the linear finite element and Quadratic finite element basis functions, a new AMG method is designed. Furthermore we give an analysis of convergence of our algebraic multigrid algorithm. The numerical results show that our new AMG method is more robust and efficient than the classical AMG method.