In this paper, a new splitting positive definite nonconforming mixed finite element method is proposed for pseudo-hyperbolic equations, in which a quasi-Wilson quadrilateral element is used for the flux p, and the bil...In this paper, a new splitting positive definite nonconforming mixed finite element method is proposed for pseudo-hyperbolic equations, in which a quasi-Wilson quadrilateral element is used for the flux p, and the bilinear element is used for u. Superconvergence results in ｜｜·｜｜div,h norm for p and optimal error estimates in L2 norm for u are derived for both semi-discrete and fully discrete schemes under almost uniform meshes.展开更多
The effects of Sn and Ga additions on the glass forming ability （GFA） of （A186LasNi9）100_xSnx（x=0, 0.2, 0.3, 0.5, 0.7, 1 and 2 at.%） and （Al86LasNi9）100_xGax（x=0, 0.2, 0.5, 1 and 1.5 at.%） alloys were system...The effects of Sn and Ga additions on the glass forming ability （GFA） of （A186LasNi9）100_xSnx（x=0, 0.2, 0.3, 0.5, 0.7, 1 and 2 at.%） and （Al86LasNi9）100_xGax（x=0, 0.2, 0.5, 1 and 1.5 at.%） alloys were systematically investigated. Unlike common microal- loying methods, both Sn and Ga have a positive heat of mixing with the main component of A1. Our analysis confirmed that proper Sn addition can suppress the strong formation of a-A1 and enhance the GFA due to the positive heat of mixing between Sn and AI and the large difference in their atomic sizes. While the addition of Ga to the base alloy acted as the nucleation cites for ct-Al and accelerated precipitation of the ct-A1 phase, thus deteriorating the GFA.展开更多
In this article, a proper orthogonal decomposition （POD） method is used to study a classical splitting positive definite mixed finite element （SPDMFE） formulation for second- order hyperbolic equations. A POD redu...In this article, a proper orthogonal decomposition （POD） method is used to study a classical splitting positive definite mixed finite element （SPDMFE） formulation for second- order hyperbolic equations. A POD reduced-order SPDMFE extrapolating algorithm with lower dimensions and sufficiently high accuracy is established for second-order hyperbolic equations. The error estimates between the classical SPDMFE solutions and the reduced-order SPDMFE solutions obtained from the POD reduced-order SPDMFE extrapolating algorithm are provided. The implementation for solving the POD reduced-order SPDMFE extrapolating algorithm is given. Some numerical experiments are presented illustrating that the results of numerical computation are consistent with theoretical conclusions, thus validating that the POD reduced-order SPDMFE extrapolating algorithm is feasible and efficient for solving second-order hyperbolic equations.展开更多
基金Supported by the National Natural Science Foundation of China(No.10971203,11271340,11101384)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20094101110006)
文摘In this paper, a new splitting positive definite nonconforming mixed finite element method is proposed for pseudo-hyperbolic equations, in which a quasi-Wilson quadrilateral element is used for the flux p, and the bilinear element is used for u. Superconvergence results in ｜｜·｜｜div,h norm for p and optimal error estimates in L2 norm for u are derived for both semi-discrete and fully discrete schemes under almost uniform meshes.
基金supported by the National Natural Science Foundation of China(Grant Nos.51010001 and 51001009)the 111 Project(Grant No.B07003)the Program for Changjiang Scholars and Innovative Research Team in University
文摘The effects of Sn and Ga additions on the glass forming ability （GFA） of （A186LasNi9）100_xSnx（x=0, 0.2, 0.3, 0.5, 0.7, 1 and 2 at.%） and （Al86LasNi9）100_xGax（x=0, 0.2, 0.5, 1 and 1.5 at.%） alloys were systematically investigated. Unlike common microal- loying methods, both Sn and Ga have a positive heat of mixing with the main component of A1. Our analysis confirmed that proper Sn addition can suppress the strong formation of a-A1 and enhance the GFA due to the positive heat of mixing between Sn and AI and the large difference in their atomic sizes. While the addition of Ga to the base alloy acted as the nucleation cites for ct-Al and accelerated precipitation of the ct-A1 phase, thus deteriorating the GFA.
基金supported by the National Science Foundation of China(11271127,11361035)Science Research of Guizhou Education Department(QJHKYZ[2013]207)Natural Science Foundation of Inner Mongolia(2012MS0106)
文摘In this article, a proper orthogonal decomposition （POD） method is used to study a classical splitting positive definite mixed finite element （SPDMFE） formulation for second- order hyperbolic equations. A POD reduced-order SPDMFE extrapolating algorithm with lower dimensions and sufficiently high accuracy is established for second-order hyperbolic equations. The error estimates between the classical SPDMFE solutions and the reduced-order SPDMFE solutions obtained from the POD reduced-order SPDMFE extrapolating algorithm are provided. The implementation for solving the POD reduced-order SPDMFE extrapolating algorithm is given. Some numerical experiments are presented illustrating that the results of numerical computation are consistent with theoretical conclusions, thus validating that the POD reduced-order SPDMFE extrapolating algorithm is feasible and efficient for solving second-order hyperbolic equations.
