A reduced-order extrapolation algorithm based on Crank-Nicolson least-squares mixed finite element （CNLSMFE） formulation and proper orthogonal decomposition （POD） technique for two-dimensional （2D） Sobolev equat...A reduced-order extrapolation algorithm based on Crank-Nicolson least-squares mixed finite element （CNLSMFE） formulation and proper orthogonal decomposition （POD） technique for two-dimensional （2D） Sobolev equations is established. The error estimates of the reduced-order CNLSMFE solutions and the implementation for the reduced-order extrapolation algorithm are provided. A numerical example is used to show that the results of numerical computations are consistent with theoretical conclusions. Moreover, it is shown that the reduced-order extrapolation algorithm is feasible and efficient for seeking numerical solutions to 2D Sobolev equations.展开更多
This paper elaborates the generation of the whole system and the ideological contents of materialistic dialectics from the aspects of building,development by Lenin and Mao Tse Tung and exploration by western Marxists,...This paper elaborates the generation of the whole system and the ideological contents of materialistic dialectics from the aspects of building,development by Lenin and Mao Tse Tung and exploration by western Marxists,demonstrating that materialistic dialectics should have two developmental clues,promoting the development of materialistic dialectics together.展开更多
基金Supported by the National Natural Science Foundation of China(11271127)Science Research Projectof Guizhou Province Education Department(QJHKYZ[2013]207)
文摘A reduced-order extrapolation algorithm based on Crank-Nicolson least-squares mixed finite element （CNLSMFE） formulation and proper orthogonal decomposition （POD） technique for two-dimensional （2D） Sobolev equations is established. The error estimates of the reduced-order CNLSMFE solutions and the implementation for the reduced-order extrapolation algorithm are provided. A numerical example is used to show that the results of numerical computations are consistent with theoretical conclusions. Moreover, it is shown that the reduced-order extrapolation algorithm is feasible and efficient for seeking numerical solutions to 2D Sobolev equations.
文摘This paper elaborates the generation of the whole system and the ideological contents of materialistic dialectics from the aspects of building,development by Lenin and Mao Tse Tung and exploration by western Marxists,demonstrating that materialistic dialectics should have two developmental clues,promoting the development of materialistic dialectics together.
