For the Poisson equation with Robin boundary conditions,by using a few techniques such as orthogonal expansion(M-type),separation of the main part and the finite element projection,we prove for the first time that the...For the Poisson equation with Robin boundary conditions,by using a few techniques such as orthogonal expansion(M-type),separation of the main part and the finite element projection,we prove for the first time that the asymptotic error expansions of bilinear finite element have the accuracy of O(h3)for u∈H3.Based on the obtained asymptotic error expansions for linear finite elements,extrapolation cascadic multigrid method(EXCMG)can be used to solve Robin problems effectively.Furthermore,by virtue of Richardson not only the accuracy of the approximation is improved,but also a posteriori error estimation is obtained.Finally,some numerical experiments that confirm the theoretical analysis are presented.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11226332,41204082 and 11071067)the China Postdoctoral Science Foundation(Grant No.2011M501295)+1 种基金the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120162120036)the Construct Program of the Key Discipline in Hunan Province
文摘For the Poisson equation with Robin boundary conditions,by using a few techniques such as orthogonal expansion(M-type),separation of the main part and the finite element projection,we prove for the first time that the asymptotic error expansions of bilinear finite element have the accuracy of O(h3)for u∈H3.Based on the obtained asymptotic error expansions for linear finite elements,extrapolation cascadic multigrid method(EXCMG)can be used to solve Robin problems effectively.Furthermore,by virtue of Richardson not only the accuracy of the approximation is improved,but also a posteriori error estimation is obtained.Finally,some numerical experiments that confirm the theoretical analysis are presented.
