二维Poisson方程谱元法有限元预条件分析
Analysis for two-dimensional finite element preconditioned spectral element method of the Poisson equation
Abstract
考虑二维Poisson方程的谱元法离散系统的预条件求解问题,利用张量积的性质,分析基于GLL×GLL节点上的双线性有限元刚性矩阵s^h作为谱元离散系统A^hU=F^h的预条件,证明了(S^hU,U)l2的等价和(A^hU,U)l2性. This paper analyze the spectrum of two-dimensional preconditional spectral element approximation to Poisson proplem. The analysis is based on the algebraic properties of the stiffness matrix(s_())of the bilinear finite element method associated to the global GLL×GLL nodes, which is used as the preconditioner of the spectral element system A_()U=F_(). We theoretically show the equivalence betweeen(S_()U, U)_(l_2) and (A_()U, U)_(l_2).