Abstract Denote by Qm the generalized quaternion group of order 4m. Let R（Qm） be its complex representation ring, and △（Qm） its augmentation ideal. In this paper, the author gives an explicit Z-basis for the △n...Abstract Denote by Qm the generalized quaternion group of order 4m. Let R（Qm） be its complex representation ring, and △（Qm） its augmentation ideal. In this paper, the author gives an explicit Z-basis for the △n（Qm） mid determines the isomorphism class of the n-th augmentation quotient for each positive integer n.展开更多
Superconvergence and recovery type a posteriori error estimators are analyzed for Pian and Sumihara's 4-node hybrid stress quadrilateral finite element method for linear elasticity problems. Superconvergence of or...Superconvergence and recovery type a posteriori error estimators are analyzed for Pian and Sumihara's 4-node hybrid stress quadrilateral finite element method for linear elasticity problems. Superconvergence of order O(h^(1+min){α,1}) is established for both the displacement approximation in H^1-norm and the stress approximation in L^2-norm under a mesh assumption, where α > 0 is a parameter characterizing the distortion of meshes from parallelograms to quadrilaterals. Recovery type approximations for the displacement gradients and the stress tensor are constructed, and a posteriori error estimators based on the recovered quantities are shown to be asymptotically exact. Numerical experiments confirm the theoretical results.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11226066,11401155)Anhui Provincial Natural Science Foundation(No.1308085QA01)
文摘Abstract Denote by Qm the generalized quaternion group of order 4m. Let R（Qm） be its complex representation ring, and △（Qm） its augmentation ideal. In this paper, the author gives an explicit Z-basis for the △n（Qm） mid determines the isomorphism class of the n-th augmentation quotient for each positive integer n.
基金supported by National Natural Science Foundation of China (Grant No. 11171239)Major Research Plan of National Natural Science Foundation of China (Grant No. 91430105)
文摘Superconvergence and recovery type a posteriori error estimators are analyzed for Pian and Sumihara's 4-node hybrid stress quadrilateral finite element method for linear elasticity problems. Superconvergence of order O(h^(1+min){α,1}) is established for both the displacement approximation in H^1-norm and the stress approximation in L^2-norm under a mesh assumption, where α > 0 is a parameter characterizing the distortion of meshes from parallelograms to quadrilaterals. Recovery type approximations for the displacement gradients and the stress tensor are constructed, and a posteriori error estimators based on the recovered quantities are shown to be asymptotically exact. Numerical experiments confirm the theoretical results.
