Supercloseness of the Divergence-Free Finite Element Solutions on Rectangular Grids  

作　　者：Yunqing Huang Shangyou Zhang 

机构地区：[1]Hunan Key Laboratory for Computation and Simulation in Science and Engineering,Xiangtan University,Xiangtan 411105,China [2]Department of Mathematical Sciences,University of Delaware,Newark,DE 19716,USA

出　　处：《Communications in Mathematics and Statistics》2013年第2期143-162,共20页数学与统计通讯（英文）

摘　　要：By the standard theory,the stable Qk+1,k−Qk,k+1/Qdck divergence-free element converges with the optimal order of approximation for the Stokes equations,but only order k for the velocity in H1-norm and the pressure in L2-norm.This is due to one polynomial degree less in y direction for the first component of velocity,which is a Qk+1,k polynomial of x and y.In this manuscript,we will show by supercloseness of the divergence free element that the order of convergence is truly k+1,for both velocity and pressure.For special solutions(if the interpolation is also divergence-free),a two-order supercloseness is shown to exist.Numerical tests are provided confirming the accuracy of the theory.

关 键 词：Mixed finite element Stokes equations Divergence-free element Quadrilateral element Rectangular grids SUPERCLOSENESS SUPERCONVERGENCE 

分 类 号：O17[理学—数学]