Shanghui Jia
Central University of Finance and Economics
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Featured researches published by Shanghui Jia.
Science China-mathematics | 2016
Shanghui Jia; Hehu Xie; Manting Xie; Fei Xu
We introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of the nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and nonlinear eigenvalue problems on the coarsest finite element space. The linearized boundary value problems are solved by some multigrid iterations. Besides the multigrid iteration, all other efficient iteration methods for solving boundary value problems can serve as the linear problem solver. We prove that the computational work of this new scheme is truly optimal, the same as solving the linear corresponding boundary value problem. In this case, this type of iteration scheme certainly improves the overfull efficiency of solving nonlinear eigenvalue problems. Some numerical experiments are presented to validate the efficiency of the new method.
Advances in Computational Mathematics | 2008
Shanghui Jia; Deli Li; Shuhua Zhang
In this paper asymptotic error expansions for mixed finite element approximations of the integro-differential equation are derived, and Richardson extrapolation is applied to improve the accuracy of the approximations by two different schemes with the help of an interpolation post-processing technique. The results of this paper provide new asymptotic expansions. As a by-product, we illustrate that all the approximations of higher accuracy can be used to form a class of a-posteriori error estimators for this mixed finite element method. Finally, a numerical example is provided to validate the theoretical results.
Applications of Mathematics | 2008
Shanghui Jia; Deli Li; Tang Liu; Shuhua Zhang
Asymptotic error expansions in the sense of L∞-norm for the Raviart-Thomas mixed finite element approximation by the lowest-order rectangular element associated with a class of parabolic integro-differential equations on a rectangular domain are derived, such that the Richardson extrapolation of two different schemes and an interpolation defect correction can be applied to increase the accuracy of the approximations for both the vector field and the scalar field by the aid of an interpolation postprocessing technique, and the key point in deriving them is the establishment of the error estimates for the mixed regularized Green’s functions with memory terms presented in R. Ewing at al., Int. J. Numer. Anal. Model 2 (2005), 301–328. As a result of all these higher order numerical approximations, they can be used to generate a posteriori error estimators for this mixed finite element approximation.
Recent Advances in Computational Sciences - Selected Papers from the International Workshop on Computational Sciences and Its Education | 2008
Shanghui Jia; Hehu Xie; Xiaobo Yin
In this paper, we derive asymptotic error expansions of eigenvalues by the mixed finite element approximations for the second order elliptic eigenvalue problems, the biharmonic eigenvalue problems and the Stokes eigenvalue problems. Extrapolation technique is applied to improve the accuracy.
Applications of Mathematics | 2009
Hongtao Chen; Shanghui Jia; Hehu Xie
Journal of Computational and Applied Mathematics | 2008
Xiaobo Yin; Hehu Xie; Shanghui Jia; Shaoqin Gao
Applications of Mathematics | 2009
Shanghui Jia; Hehu Xie; Xiaobo Yin; Shaoqin Gao
Numerical Methods for Partial Differential Equations | 2008
Shanghui Jia; Hehu Xie; Xiaobo Yin; Shaoqin Gao
Applied Numerical Mathematics | 2011
Hongtao Chen; Shanghui Jia; Hehu Xie
Science China-mathematics | 2013
Shanghui Jia; Hongtao Chen; Hehu Xie