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1.
一种半隐式有限体积—有限元方法的收敛性   总被引:1,自引:0,他引:1  
本文研究非线性对流扩散问题的一种半隐式有限体积和有限元方法相结合的数值方法,给出数值解的收敛性及其证明。  相似文献   

2.
对流扩散方程的一种显式有限体积——有限元方法   总被引:4,自引:0,他引:4  
本文给出非线性对流扩散问题的一种有限体积的有限元方法相结合的显式离散方法,证明了数值解的稳定性,并给出了一个实际算例。  相似文献   

3.
半导体瞬态问题的数学模型是由四个方程组成的非线性偏微分方程组的初边值问题所决定.其中电子浓度和空穴浓度方程往往是对流占优扩散问题,普通的方法已不适用,为此本文用迎风格式处理对流项部分,提出一种全离散迎风有限体积元方法,并进行收敛性分析,在最一般的情况下得到了一阶精度L2模误差估计结果.  相似文献   

4.
使用Arnold等人提出的求解椭圆方程的间断有限元的一般框架及新的处理非线性对流项的方法,得到了非线性对流扩散方程的三层隐-显hp-LDG方法的误差估计.对Burgers方程进行了数值计算,计算结果验证了文中得到的理论结果.  相似文献   

5.
王同科 《应用数学》2004,17(4):544-550
本文针对一维定常型对流占优扩散方程提出了一类迎风有限体积格式 .该格式对对流项具有二阶精度 ,对扩散项保持一阶精度 ,符合对流占优扩散问题强对流、弱扩散的特点 .  相似文献   

6.
对于线性对流占优扩散方程,采用特征线有限元方法离散时间导数项和对流项,用分片线性有限元离散空间扩散项,并给出了一致的后验误差估计,其中估计常数不依赖与扩散项系数。  相似文献   

7.
通过使用Arnold等人和Perugia等人对于椭圆问题引入的提升算子方法以及不同的处理非线性对流项的方法,得到了对流-扩散方程的hp-局部间断Galerkin有限元(hp-LDG)方法的最优L~∞(H~1)误差估计.对于非线性Burgers方程进行了数值试验,计算结果验证了文中得到的理论结果.  相似文献   

8.
文宗川  郭彦  梁静国  李宏 《应用数学》2007,20(4):791-800
考虑KdV方程的两种特征线性混合间断有限元方法,一种方法建立在标准特征线修正方法的基础上,另一种方法是带有对流项修正的特征线修正方法.利用具有实际物理意义的特征线追踪技巧处理时间导数项和对流项,采用混合间断有限元方法处理三阶导数项,分别证明了两种方法有限元解的唯一性、稳定性和误差估计.  相似文献   

9.
窦红 《大学数学》2002,18(5):29-32
给出求解一种二维非线性对流扩散方程组的 Grank-Nicolson型特征有限元方法 ,并给出该方法的 H1模最优阶误差估计 .  相似文献   

10.
窦红 《工科数学》2002,18(5):29-32
给出求解一种二维非线性对流扩散方程组的Grank-Nicolson型特征有限元方法,并给出该方法的H^1模最优误差估计。  相似文献   

11.
In this article, a characteristic finite volume element method is presented for solving air pollution models. The convection term is discretized using the characteristic method and diffusion term is approximated by finite volume element method. Compared with standard finite volume element method, our proposed method is more accurate and efficient, especially suitable to solve convection-dominated problems. The proposed numerical schemes are analyzed for convergence in L 2 norm. Some numerical results are presented to demonstrate the efficiency and accuracy of the method.  相似文献   

12.
The L 2-penalty fictitious domain method is based on a reformulation of the original problem in a larger simple-shaped domain by introducing a discontinuous reaction term with a penalty parameter ε > 0. We first derive regularity results and some a priori estimates and then prove several error estimates. We also give several error estimates for discretization problems by the finite element and finite volume methods.  相似文献   

13.
In this work, a dual porosity model of reactive solute transport in porous media is presented. This model consists of a nonlinear-degenerate advection-diffusion equation including equilibrium adsorption to the reaction combined with a first-order equation for the non-equilibrium adsorption interaction processes. The numerical scheme for solving this model involves a combined high order finite volume and finite element scheme for approximation of the advection-diffusion part and relaxation-regularized algorithm for nonlinearity-degeneracy. The combined finite volume-finite element scheme is based on a new formulation developed by Eymard et al. (2010) [10]. This formulation treats the advection and diffusion separately. The advection is approximated by a second-order local maximum principle preserving cell-vertex finite volume scheme that has been recently proposed whereas the diffusion is approximated by a finite element method. The result is a conservative, accurate and very flexible algorithm which allows the use of different mesh types such as unstructured meshes and is able to solve difficult problems. Robustness and accuracy of the method have been evaluated, particularly error analysis and the rate of convergence, by comparing the analytical and numerical solutions for first and second order upwind approaches. We also illustrate the performance of the discretization scheme through a variety of practical numerical examples. The discrete maximum principle has been proved.  相似文献   

14.
Two-grid methods for characteristic finite volume element solutions are presented for a kind of semilinear convection-dominated diffusion equations. The methods are based on the method of characteristics, two-grid method and the finite volume element method. The nonsymmetric and nonlinear iterations are only executed on the coarse grid (with grid size H). And the fine-grid solution (with grid size h) can be obtained by a single symmetric and linear step. It is proved that the coarse grid can be much coarser than the fine grid. The two-grid methods achieve asymptotically optimal approximation as long as the mesh sizes satisfy H = O(h1/3).  相似文献   

15.
《Applied Mathematical Modelling》2014,38(7-8):2265-2279
This paper details the evaluation and enhancement of the vertex-centred finite volume method for the purpose of modelling linear elastic structures undergoing bending. A matrix-free edge-based finite volume procedure is discussed and compared with the traditional isoparametric finite element method via application to a number of test-cases. It is demonstrated that the standard finite volume approach exhibits similar disadvantages to the linear Q4 finite element formulation when modelling bending. An enhanced finite volume approach is proposed to circumvent this and a rigorous error analysis conducted. It is demonstrated that the developed finite volume method is superior to both standard finite volume and Q4 finite element methods, and provides a practical alternative to the analysis of bending-dominated solid mechanics problems.  相似文献   

16.
In this paper, we consider the finite volume element method based on the Crouzeix–Raviart element and prove the existence, uniqueness and uniform convergence of the finite volume element approximations for the non-self-adjoint and indefinite elliptic problems under minimal elliptic regularity assumption.  相似文献   

17.
This paper is concerned with the analysis of a finite element method for nonhomogeneous second order elliptic interface problems on smooth domains. The method consists in approximating the domains by polygonal domains, transferring the boundary data in a natural way, and then applying a finite element method to the perturbed problem on the approximate polygonal domains. It is shown that the error in the finite element approximation is of optimal order for linear elements on a quasiuniform triangulation. As such the method is robust in the regularity of the data in the original problem.  相似文献   

18.
The combined finite volume–finite element scheme for a double nonlinear parabolic convection-dominated diffusion equation which models the variably saturated flow and contaminant transport problems in porous media is extended. Whereas the convection is approximated by a finite volume method (Multi-Point Flux Approximation), the diffusion is approximated by a finite element method. The scheme is fully implicit and involves a relaxation-regularized algorithm. Due to monotonicity and conservation properties of the approximated scheme and in view of the compactness theorem we show the convergence of the numerical scheme to the weak solution. Our scheme is applied for computing two dimensional examples with different degrees of complexity. The numerical results demonstrate that the proposed scheme gives good performance in convergence and accuracy.  相似文献   

19.
本文利用齐次定解条件对定常不可压Navier—Stokes方程的非线性项进行处理,给出了相应的一种迎风Galerkin有限元算法;针对这种迎风Galerkin有限元算法,在迎风参数满足一定条件下,利用其三项式具有的一些很好性质,更简单地证明了该问题解的存在唯一性。  相似文献   

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