芮洪兴
微分方程数值解法,区域分裂及并行算法,油水资源数值模拟方法及应用软件
个性化签名
- 姓名:芮洪兴
- 目前身份:
- 担任导师情况:
- 学位:
-
学术头衔:
博士生导师
- 职称:-
-
学科领域:
计算数学
- 研究兴趣:微分方程数值解法,区域分裂及并行算法,油水资源数值模拟方法及应用软件
1984年在山东大学获理学学士学位。1987年在山东大学获理学硕士学位并留校任教。1990年考取在职博士生, 1994年7月获理学博士学位。1994年12起在山东大学任副教授。2000年10月至今在山东大学任教授。2001年12月被聘为博士生导师。主要研究微分方程数值解法,区域分裂及并行算法,油水资源数值模拟方法及应用软件。在有限元方法,混合元方法,有限体积方法,区域分解并行算法,最小二乘有限元,多孔介质流体流动以及油水资源数值模拟方法研究方面发表论文50余篇。作为负责人已完成和正承担国家自然科学基金项目,教育部博士点基金,山东省自然科学基金项目多项。在应用软件方面已完成国家“八五”攻关及石油部“八五”攻关项目各一项。
-
主页访问
3608
-
关注数
0
-
成果阅读
374
-
成果数
8
【期刊论文】An Expanded Mixed Covolume Method for Elliptic Problems
芮洪兴, Hongxing Rui, Tongchao Lu
,-0001,():
-1年11月30日
We consider the mixed covolume method combining with the expanded mixed element for a system of first-order partial differential equations resulting from the mixed formulation of a general self-adjoint elliptic problem with a full diffusion tensor. The system can be used to model the transport of a contaminant carried by a flow in porous media. We use the lowest order Raviart-Thomas mixed element space. We show the first-order error estimate for the approximate solution in L2 norm. We show the superconvergence both for pressure and velocity in certain discrete norms. We also get a finite difference scheme by using proper approximate integration formulas. Finally we give some numerical examples.
mixed covolume method, expanded mixed element, elliptic problem, error estimate, superconvergence
-
47浏览
-
0点赞
-
0收藏
-
0分享
-
241下载
-
0评论
-
引用
【期刊论文】Least-squares Galerkin procedures for parabolic integro-differential equations
芮洪兴, Hui Guo, Hongxing Rui*
Applied Mathematics and Computation 150 (2004) 749-762,-0001,():
-1年11月30日
Two least-squares Galerkin finite element schemes are formulated to solve parabolic integro-differential equations. The advantage of this method is that it is not subject to the LBB condition. The convergence analysis shows that the least-squares mixed element schemes yield the approximate solution with optimal accuracy in H(div; Ω)×H1(Ω)and (L2(Ω))2×L2(Ω), respectively.
Least-squares Galerkin finite element, Parabolic integro-differential equation, Convergence analysis
-
72浏览
-
0点赞
-
0收藏
-
0分享
-
221下载
-
0评论
-
引用
芮洪兴, Hongxing Rui
,-0001,():
-1年11月30日
Consider the following convection di.usion equation,{∂u/∂t+ b1(x; y) ∂u/∂x+ b2(y) ∂u/∂y-(a1∂2u/∂x2 + a2∂2u/∂y2) = f in Ω×J, u(x; y; t) = φ(x; t) onΩ×J,u(x; y; 0) = u0(x; y) inΩ(1)} whereΩ= (0, 1) × (0, 1), J = (0, T), b1(x; y), b2(y) are smooth functions and a1; a2 are positive constants. When convection dominates di.usion, i.e. 0 < a1; a2 << |b|, the general finite di.erence or finite element methods often result numerical oscillation[1]. The upwind method is an e¡Àcient method but is only first order accurate. For one dimensional stable problem with constant coe¡Àcient, [3] presented a high order upwind scheme, but it is di¡Àcult to extend the method to variable coe¡Àcient problem and two dimensional problem. In this paper we give an alternative direction iterative method combining with one dimensional second order upwind scheme for two dimensional problem. It can be as a high speed algorithm on parallel computer. The maximum principle and the second order uniform norm error estimate are obtained. Finally we give some numerical examples.
Upwind Scheme,, convection-diffusion,, error estimate
-
83浏览
-
0点赞
-
0收藏
-
0分享
-
404下载
-
0评论
-
引用
【期刊论文】Multiplicative Schwarz methods for parabolic problems ☆
芮洪兴, Hongxing Rui
Applied Mathematics and Computation 136(2003)593-610,-0001,():
-1年11月30日
Based on domain decomposition, we give a multiplicative Schwarz domain decomposition method for semi-linear parabolic problems. We consider the relation between the convergence rate and discretization parameters, including the diameter of the subdomain. We give the error estimate, which tells us that the convergence of the approximate solution is independent of the iteration number at each time level. Finally we give a numerical example.
Multiplicative Schwarz method, Parabolic equation, Error estimate
-
41浏览
-
0点赞
-
0收藏
-
0分享
-
143下载
-
0评论
-
引用
【期刊论文】Symmetric Mixed Covolume Methods for Parabolic Problems
芮洪兴, Hongxing Rui
,-0001,():
-1年11月30日
We present a mixed covolume method for a system of first order partial differential equations resulting from the mixed formulation of the general self-adjoint parabolic problem with a variable nondiagonal diffusion tensor. The lowest order Raviart-Thomas mixed element space on rectangles is used. We prove the first order optimal rate of convergence for approximate pressure as well as for approximate velocity. We also prove the second order superconvergence both for approximate velocity and pressure in certain discrete norms.
symmetric, mixed covolume method, parabolic equation, error estimate, superconvergence
-
48浏览
-
0点赞
-
0收藏
-
0分享
-
194下载
-
0评论
-
引用
【期刊论文】A second order characteristic finite element scheme for convection-diffusion problems
芮洪兴, Hongxing Rui, Masahisa Tabata
,-0001,():
-1年11月30日
A new characteristic finite element scheme is presented for convection-diffusion problems. It is of second order accuracy in time increment, symmetric, and unconditionally stable. Optimal error estimates are proved in the framework of L2-theory. Numerical results are presented for two examples, which show the advantage of the scheme.
-
33浏览
-
0点赞
-
0收藏
-
0分享
-
140下载
-
0评论
-
引用
芮洪兴, Hongxing Rui
Journal of Computational and Applied Mathematics 146(2002)373-386,-0001,():
-1年11月30日
The &nite volume element method is a discretization technique for partial di3erential equations, but in general case the coe5cient matrix of its linear system is not symmetric, even for the self-adjoint continuous problem. In this paper we develop a kind of symmetric modi&ed &nite volume element methods both for general self-adjoint elliptic and for parabolic problems on general discretization, their coe5cient matrix are symmetric. We give the optimal order energy norm error estimates. We also prove that the di3erence between the solutions of the &nite volume element method and symmetric modi&ed &nite volume element method is a high order term.
Symmetric coeffcient matrix, Finite volume element, Error estimates 1.,
-
0浏览
-
0点赞
-
0收藏
-
0分享
-
116下载
-
0评论
-
引用
【期刊论文】NONOVERLAPPING DOMAIN DECOMPOSITION METHOD WITH MIXED ELEMENT FOR ELLIPTIC PROBLEMS*
芮洪兴, Rui Hongxing
,-0001,():
-1年11月30日
In this paper we consider the nonoverlapping domain decomposition method based on mixed element approximation for elliptic problems in two dimentional space. We give a kind of discrete domain decomposition iterative algorithm using mixed finite element, the subdomain problems of which can be implemented parallelly. We also give the existence, uniqueness and convergence of the approximate solution.
-
50浏览
-
0点赞
-
0收藏
-
0分享
-
136下载
-
0评论
-
引用