Advances in Numerical Analysis
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The latest articles from Hindawi Publishing Corporation
© 2014 , Hindawi Publishing Corporation . All rights reserved.

An Efficient Family of TraubSteffensenType Methods for Solving Systems of Nonlinear Equations
Wed, 02 Jul 2014 09:14:36 +0000
http://www.hindawi.com/journals/ana/2014/152187/
Based on TraubSteffensen method, we present a derivative free threestep family of sixthorder methods for solving systems of nonlinear equations. The local convergence order of the family is determined using firstorder divided difference operator for functions of several variables and direct computation by Taylor's expansion. Computational efficiency is discussed, and a comparison between the efficiencies of the proposed techniques with the existing ones is made. Numerical tests are performed to compare the methods of the proposed family with the existing methods and to confirm the theoretical results. It is shown that the new family is especially efficient in solving large systems.
Janak Raj Sharma and Puneet Gupta
Copyright © 2014 Janak Raj Sharma and Puneet Gupta. All rights reserved.

On Nonlinear Inverse Problems of Heat Transfer with Radiation Boundary Conditions: Application to Dehydration of Gypsum Plasterboards Exposed to Fire
Sun, 13 Apr 2014 13:39:37 +0000
http://www.hindawi.com/journals/ana/2014/634712/
The paper investigates boundary optimal controls and parameter estimates to the wellposedness nonlinear model of dehydration of thermic problems. We summarize the general formulations for the boundary control for initialboundary value problem for nonlinear partial differential equations modeling the heat transfer and derive necessary optimality conditions, including the adjoint equation, for the optimal set of parameters minimizing objective functions . Numerical simulations illustrate several numerical optimization methods, examples, and realistic cases, in which several interesting phenomena are observed. A large amount of computational effort is required to solve the coupled state equation and the adjoint equation (which is backwards in time), and the algebraic gradient equation (which implements the coupling between the adjoint and control variables). The state and adjoint equations are solved using the finite element method.
A. Belmiloudi and F. Mahé
Copyright © 2014 A. Belmiloudi and F. Mahé. All rights reserved.

General Family of Third Order Methods for Multiple Roots of Nonlinear Equations and Basin Attractors for Various Methods
Mon, 31 Mar 2014 16:39:23 +0000
http://www.hindawi.com/journals/ana/2014/963878/
A general scheme of third order convergence is described for finding multiple roots of nonlinear equations. The proposed scheme requires one evaluation of , and each per iteration and contains several known onepoint third order methods for finding multiple roots, as particular cases. Numerical examples are included to confirm the theoretical results and demonstrate convergence behavior of the proposed methods. In the end, we provide the basins of attraction for some methods to observe their dynamics in the complex plane.
Rajni Sharma and Ashu Bahl
Copyright © 2014 Rajni Sharma and Ashu Bahl. All rights reserved.

Monotonicity Preserving Rational Quadratic Fractal Interpolation Functions
Thu, 30 Jan 2014 07:25:34 +0000
http://www.hindawi.com/journals/ana/2014/504825/
Fractal interpolation is an advanced technique for analysis and synthesis of scientific and engineering data. We introduce the rational quadratic fractal interpolation functions (FIFs) through a suitable rational quadratic iterated function system (IFS). The novel notion
of shape preserving fractal interpolation without any shape parameter is introduced through the rational fractal interpolation model in the literature for the first time. For a prescribed set of monotonic data, we derive the sufficient conditions by restricting the scaling factors for shape preserving rational quadratic FIFs. A local modification pertaining to any subinterval is possible in this model if the scaling factors are chosen appropriately. We establish the convergence results of a monotonic rational quadratic FIF to the original function in . For given data with derivatives at grids, our approach generates several monotonicity preserving rational quadratic FIFs, whereas this flexibility is not available in the classical approach. Finally, numerical experiments support the importance of the developed rational quadratic IFS scheme through construction of visually pleasing monotonic rational fractal curves including
the classical one.
A. K. B. Chand and N. Vijender
Copyright © 2014 A. K. B. Chand and N. Vijender. All rights reserved.

Nonlinear DoubleLayer Bragg Waveguide: Analytical and Numerical Approaches to Investigate Waveguiding Problem
Wed, 22 Jan 2014 08:08:52 +0000
http://www.hindawi.com/journals/ana/2014/231498/
The paper is concerned with propagation of surface TE waves in a circular nonhomogeneous twolayered dielectric waveguide filled with nonlinear medium. The problem is reduced to the analysis of a
nonlinear integral equation with a kernel in the form of the Green function. The existence of propagating TE waves for chosen nonlinearity (the Kerr law) is proved using the contraction mapping method. Conditions under which k waves can propagate are obtained, and intervals of localization of the corresponding propagation constants are found. For numerical solution of the problem, a method based on solving an auxiliary Cauchy problem (the shooting method) is proposed. In numerical experiment, two types of nonlinearities are considered and compared: the Kerr nonlinearity and nonlinearity with saturation. New propagation regime is found.
Yury G. Smirnov, Eugenii Yu. Smol’kin, and Dmitry V. Valovik
Copyright © 2014 Yury G. Smirnov et al. All rights reserved.

A New Upper Bound for of a Strictly Diagonally Dominant Matrix
Thu, 26 Dec 2013 15:23:54 +0000
http://www.hindawi.com/journals/ana/2013/980615/
A new upper bound for of a real strictly diagonally dominant matrix is present, and a new lower bound of the smallest eigenvalue of is given, which improved the results in the literature. Furthermore, an upper bound for of a real strictly diagonally dominant matrix is shown.
Zhanshan Yang, Bing Zheng, and Xilan Liu
Copyright © 2013 Zhanshan Yang et al. All rights reserved.

Numerical Method for Solving Matrix Coefficient Elliptic Equation on Irregular Domains with SharpEdged Boundaries
Tue, 24 Dec 2013 09:51:56 +0000
http://www.hindawi.com/journals/ana/2013/967342/
We present a new secondorder accurate numerical method for solving matrix coefficient elliptic equation on irregular domains with
sharpedged boundaries. Nontraditional finite element method with nonbodyfitting grids is implemented on a fictitious domain in which the irregular domains are embedded. First we set the function and coefficient in the fictitious part, and the nonsmooth boundary is then treated as an interface. The emphasis is on the construction of jump conditions on the interface; a special position for the ghost point is chosen so that the method is more accurate. The test function basis is chosen to be the standard finite element basis independent of the interface, and the solution basis is chosen to be piecewise linear satisfying the jump conditions across the interface. This is an efficient method for dealing with elliptic equations in irregular domains with nonsmooth boundaries, and it is able to treat the general case of matrix coefficient. The complexity and computational expense
in mesh generation is highly decreased, especially for moving boundaries, while robustness, efficiency, and accuracy are promised. Extensive numerical
experiments indicate that this method is secondorder accurate in the norm in both two and three dimensions and numerically very stable.
Liqun Wang and Liwei Shi
Copyright © 2013 Liqun Wang and Liwei Shi. All rights reserved.

A ProperOrthogonal Decomposition Variational Multiscale Approximation Method for a Generalized Oseen Problem
Wed, 18 Dec 2013 13:13:31 +0000
http://www.hindawi.com/journals/ana/2013/974284/
We introduce the variational multiscale (VMS) stabilization for the reducedorder modeling of incompressible flows. It is well known that the proper orthogonal decomposition (POD) technique in reducedorder modeling experiences numerical instability when applied to complex flow problems. In this case a POD discretization naturally separates out structures which corresponding to the energy cascade on large and small scales, in order, a VMS approach is natural. In this paper, we provide the mathematical background necessary for implementing VMS to a PODGalerkin model of a generalized Oseen problem. We provide theoretical evidence which indicates the consistency of utilizing a VMS approach in the stabilization of reduced order flows. In addition we provide numerical experiments indicating that VMS improves fidelity in reproducing the qualitative properties of the flow.
John Paul Roop
Copyright © 2013 John Paul Roop. All rights reserved.

A New Extended Padé Approximation and Its Application
Tue, 10 Dec 2013 12:02:37 +0000
http://www.hindawi.com/journals/ana/2013/263467/
We extend ordinary Padé approximation, which is based on a set of standard polynomials as , to a new extended Padé approximation (Müntz Padé approximation), based on the general basic function set (the particular case of Müntz polynomials) using general Taylor series (based on fractional calculus) with error convergency. The importance of this extension is that the ordinary Padé approximation is a particular case of our extended Padé approximation. Also the parameterization ( is the corresponding parameter) of new extended Padé approximation is an important subject which, obtaining the optimal value of this parameter, can be a good question for a new research.
Z. Kalateh Bojdi, S. AhmadiAsl, and A. Aminataei
Copyright © 2013 Z. Kalateh Bojdi et al. All rights reserved.

Some Results on Preconditioned MixedType Splitting Iterative Method
Tue, 03 Dec 2013 13:54:44 +0000
http://www.hindawi.com/journals/ana/2013/512084/
We present a preconditioned mixedtype splitting iterative method for solving the linear system , where is a Zmatrix. And we give some comparison theorems to show that the rate of convergence of the preconditioned mixedtype splitting iterative method is faster than that of the mixedtype splitting iterative method. Finally, we give one numerical example to illustrate our results.
Guangbin Wang and Fuping Tan
Copyright © 2013 Guangbin Wang and Fuping Tan. All rights reserved.

On Some Efficient Techniques for Solving Systems of Nonlinear Equations
Thu, 31 Oct 2013 11:47:05 +0000
http://www.hindawi.com/journals/ana/2013/252798/
We present iterative methods of convergence order three, five, and six for solving systems of nonlinear equations. Thirdorder method is composed of two steps, namely, Newton iteration as the first step and weightedNewton iteration as the second step. Fifth and sixthorder methods are composed of three steps of which the first two steps are same as that of the thirdorder method whereas the third is again a weightedNewton step. Computational efficiency in its general form is discussed and a comparison between the efficiencies of proposed techniques with existing ones is made. The performance is tested through numerical examples. Moreover, theoretical results concerning order of convergence and computational efficiency are verified in the examples. It is shown that the present methods have an edge over similar existing methods, particularly when applied to large systems of equations.
Janak Raj Sharma and Puneet Gupta
Copyright © 2013 Janak Raj Sharma and Puneet Gupta. All rights reserved.

Geometric Mesh ThreePoint Discretization for FourthOrder Nonlinear Singular Differential Equations in Polar System
Thu, 24 Oct 2013 11:09:33 +0000
http://www.hindawi.com/journals/ana/2013/614508/
Numerical method based on three geometric stencils has been proposed for the numerical solution of nonlinear singular fourthorder ordinary differential equations. The method can be easily extended to the sixthorder differential equations. Convergence analysis proves the thirdorder convergence of the proposed scheme. The resulting difference equations lead to block tridiagonal matrices and can be easily solved using block GaussSeidel algorithm. The computational results are provided to justify the usefulness and reliability of the proposed method.
Navnit Jha, R. K. Mohanty, and Vinod Chauhan
Copyright © 2013 Navnit Jha et al. All rights reserved.

A Global Convergence of LSCD Hybrid Conjugate Gradient Method
Tue, 22 Oct 2013 08:26:11 +0000
http://www.hindawi.com/journals/ana/2013/517452/
Conjugate gradient method is one of the most effective algorithms for solving unconstrained optimization problem. In this paper, a modified conjugate gradient method is presented and analyzed which is a hybridization of known LS and CD conjugate gradient algorithms. Under some mild conditions, the Wolfetype line search can guarantee the global convergence of the LSCD method. The numerical results show that the algorithm is efficient.
Xiangfei Yang, Zhijun Luo, and Xiaoyu Dai
Copyright © 2013 Xiangfei Yang et al. All rights reserved.

Convergent Homotopy Analysis Method for Solving Linear Systems
Tue, 08 Oct 2013 08:34:16 +0000
http://www.hindawi.com/journals/ana/2013/732032/
By using homotopy analysis method (HAM), we introduce an iterative method for solving linear systems. This method (HAM) can be used to accelerate the convergence of the basic iterative methods. We also show that by applying HAM to a divergent iterative scheme, it is possible to construct a convergent homotopyseries solution when the iteration matrix G of the iterative scheme has particular properties such as being symmetric, having real eigenvalues. Numerical experiments are given to show the efficiency of the new method.
H. Nasabzadeh and F. Toutounian
Copyright © 2013 H. Nasabzadeh and F. Toutounian. All rights reserved.

New Nonpolynomial Spline in Compression Method of for the Solution of 1D Wave Equation in Polar Coordinates
Mon, 30 Sep 2013 12:50:43 +0000
http://www.hindawi.com/journals/ana/2013/470480/
We propose a threelevel implicit nine point compact finite difference formulation of order two in time and four in space direction, based on nonpolynomial spline in compression approximation in direction and finite difference approximation in direction for the numerical solution of onedimensional wave equation in polar coordinates. We describe the mathematical formulation procedure in detail and also discussed the stability of the method. Numerical results are provided to justify the usefulness of the proposed method.
Venu Gopal, R. K. Mohanty, and Navnit Jha
Copyright © 2013 Venu Gopal et al. All rights reserved.

Iterative Method for Solving a Beam Equation with Nonlinear Boundary Conditions
Wed, 28 Aug 2013 11:27:21 +0000
http://www.hindawi.com/journals/ana/2013/470258/
In this paper, we propose an iterative method for solving a beam problem which is described by a nonlinear fourthorder equation with nonlinear boundary conditions. The method reduces this nonlinear fourthorder problem to a sequence of linear secondorder problems with linear boundary conditions. The convergence of the method is proved, and some numerical examples demonstrate the efficiency of the method.
Quang A. Dang and Nguyen Thanh Huong
Copyright © 2013 Quang A. Dang and Nguyen Thanh Huong. All rights reserved.

Codimensionm Bifurcation Theorems Applicable to the Numerical Verification Methods
Thu, 27 Jun 2013 11:59:43 +0000
http://www.hindawi.com/journals/ana/2013/420897/
We establish codimensionm bifurcation theorems applicable to the numerical verification methods. They are generalization of codimension1 bifurcation theorems established by (Kawanago, 2004). As a numerical example, we treat Hopf bifurcation, which is codimension2 bifurcation.
Tadashi Kawanago
Copyright © 2013 Tadashi Kawanago. All rights reserved.

Mixed Finite Element Methods for the Poisson Equation Using Biorthogonal and QuasiBiorthogonal Systems
Thu, 11 Apr 2013 17:54:10 +0000
http://www.hindawi.com/journals/ana/2013/189045/
We introduce two threefield mixed formulations for the Poisson equation and propose finite element methods for their approximation. Both mixed formulations are obtained by introducing a weak equation for the gradient of the solution by means of a Lagrange multiplier space. Two efficient numerical schemes are proposed based on using a pair of bases for the gradient of the solution and the Lagrange multiplier space forming biorthogonal and quasibiorthogonal systems, respectively. We also establish an optimal a priori error estimate for both finite element approximations.
Bishnu P. Lamichhane
Copyright © 2013 Bishnu P. Lamichhane. All rights reserved.

Three New Optimal FourthOrder Iterative Methods to Solve Nonlinear Equations
Sun, 24 Mar 2013 09:02:14 +0000
http://www.hindawi.com/journals/ana/2013/957496/
We present new modifications to Newton's method for solving nonlinear equations. The analysis of convergence shows that these methods have fourthorder convergence. Each of the three methods uses three functional evaluations. Thus, according to KungTraub's conjecture, these are optimal methods. With the previous ideas, we extend the analysis to functions with multiple roots. Several numerical examples are given to illustrate that the presented methods have better performance compared with Newton's classical method and other methods of fourthorder convergence recently published.
Gustavo FernándezTorres and Juan VásquezAquino
Copyright © 2013 Gustavo FernándezTorres and Juan VásquezAquino. All rights reserved.

On a Fast Convergence of the RationalTrigonometricPolynomial Interpolation
Thu, 21 Mar 2013 18:51:45 +0000
http://www.hindawi.com/journals/ana/2013/315748/
We consider the convergence acceleration of the KrylovLanczos interpolation by rational correction functions and investigate convergence of the resultant parametric rationaltrigonometricpolynomial interpolation. Exact constants of asymptotic errors are obtained in the regions away from discontinuities, and fast convergence of the rationaltrigonometricpolynomial interpolation compared to the KrylovLanczos interpolation is observed. Results of numerical experiments confirm theoretical estimates and show how the parameters of the interpolations can be determined in practice.
Arnak Poghosyan
Copyright © 2013 Arnak Poghosyan. All rights reserved.

A TwoPoint Newton Method Suitable for Nonconvergent Cases and with SuperQuadratic Convergence
Tue, 19 Mar 2013 13:53:34 +0000
http://www.hindawi.com/journals/ana/2013/687382/
An iterative formula based on Newton’s method alone is presented for the iterative solutions of equations that ensures convergence in cases where the traditional Newton Method may fail to converge to the desired root. In addition, the method has superquadratic convergence of order 2.414 (i.e., ). Newton method is said to fail in certain cases leading to oscillation, divergence to increasingly large number, or offshooting away to another root further from the desired domain or offshooting to an invalid domain where the function may not be defined. In addition when the derivative at the iteration point is zero, Newton method stalls. In most of these cases, hybrids of several methods such as Newton, bisection, and secant methods are suggested as substitute methods and Newton method is essentially blended with other methods or altogether abandoned. This paper argues that a solution is still possible in most of these cases by the application of Newton method alone without resorting to other methods and with the same computational effort (two functional evaluations per iteration) like the traditional Newton method. In addition, the proposed modified formula based on Newton method has better convergence characteristics than the traditional Newton method.
Ababu Teklemariam Tiruneh, W. N. Ndlela, and S. J. Nkambule
Copyright © 2013 Ababu Teklemariam Tiruneh et al. All rights reserved.

Modified Bézier Curves with ShapePreserving Characteristics Using Differential Evolution Optimization Algorithm
Wed, 13 Mar 2013 17:54:31 +0000
http://www.hindawi.com/journals/ana/2013/858279/
A parametric equation for a modified Bézier curve is proposed for curve fitting applications. The proposed equation contains shaping parameters to adjust the shape of the fitted curve. This flexibility of shape control is expected to produce a curve which is capable of following any sets of discrete data points. A Differential Evolution (DE) optimization based technique is proposed to find the optimum value of these shaping parameters. The optimality of the fitted curve is defined in terms of some proposed cost parameters. These parameters are defined based on sum of squares errors. Numerical results are presented highlighting the effectiveness of the proposed curves compared with conventional Bézier curves. From the obtained
results, it is observed that the proposed method produces a curve that fits the data points more accurately.
Mohammad Asif Zaman and Shuvro Chowdhury
Copyright © 2013 Mohammad Asif Zaman and Shuvro Chowdhury. All rights reserved.

Nonlinear Finite Element Analysis of Sloshing
Wed, 27 Feb 2013 13:31:19 +0000
http://www.hindawi.com/journals/ana/2013/571528/
The disturbance on the free surface of the liquid when the liquidfilled tanks are excited is called sloshing. This paper examines the nonlinear sloshing response of the liquid free surface in partially filled twodimensional rectangular tanks using finite element method. The liquid is assumed to be inviscid, irrotational, and incompressible; fully nonlinear potential wave theory is considered and mixed EulerianLagrangian scheme is adopted. The velocities are obtained from potential using least square method for accurate evaluation. The fourthorder RungeKutta method is employed to advance the solution in time. A regridding technique based on cubic spline is employed to avoid numerical instabilities. Regular harmonic excitations and random excitations are used as the external disturbance to the container. The results obtained are compared with published results to validate the numerical method developed.
Siva Srinivas Kolukula and P. Chellapandi
Copyright © 2013 Siva Srinivas Kolukula and P. Chellapandi. All rights reserved.

Modular Analysis of Sequential Solution Methods for Almost Block Diagonal Systems of Equations
Sun, 24 Feb 2013 07:56:20 +0000
http://www.hindawi.com/journals/ana/2013/563872/
Almost block diagonal linear systems of equations can be exemplified by two modules. This makes it possible to construct all sequential forms of band and/or block elimination methods. It also allows easy assessment of the methods on the basis of their operation counts, storage needs, and admissibility of partial pivoting. The outcome of the analysis and implementation is to discover new methods that outperform a wellknown method, a modification of which is, therefore, advocated.
Tarek M. A. ElMistikawy
Copyright © 2013 Tarek M. A. ElMistikawy. All rights reserved.

Parallel Nonoverlapping DDM Combined with the Characteristic Method for Incompressible Miscible Displacements in Porous Media
Tue, 19 Feb 2013 09:51:26 +0000
http://www.hindawi.com/journals/ana/2013/303952/
Two types of approximation schemes are established for incompressible miscible
displacements in porous media. First, standard mixed finite element method is used
to approximate the velocity and pressure. And then parallel nonoverlapping domain
decomposition methods combined with the characteristics method are presented for
the concentration. These methods use the characteristic method to handle the material
derivative term of the concentration equation in the subdomains and explicit flux
calculations on the interdomain boundaries by integral mean method or extrapolation
method to predict the innerboundary conditions. Thus, the velocity and pressure can
be approximated simultaneously, and the parallelism can be achieved for the concentration
equation. The explicit nature of the flux prediction induces a time step limitation
that is necessary to preserve stability. These schemes hold the advantages of nonoverlapping
domain decomposition methods and the characteristic method. Optimal
error estimates in norm are derived for these two schemes, respectively.
Keying Ma and Tongjun Sun
Copyright © 2013 Keying Ma and Tongjun Sun. All rights reserved.

New Approach for Solving a Class of Doubly Singular TwoPoint Boundary Value Problems Using Adomian Decomposition Method
Wed, 26 Dec 2012 14:35:44 +0000
http://www.hindawi.com/journals/ana/2012/541083/
We propose two new modified recursive schemes for solving a class of doubly singular twopoint boundary value problems. These schemes are based on Adomian decomposition method (ADM) and new proposed integral operators. We use all the boundary conditions to derive an integral equation before establishing the recursive schemes for the solution components. Thus we develop recursive schemes without any undetermined coefficients while computing successive solution components, whereas several previous recursive schemes have done so. This modification also avoids solving a sequence of nonlinear algebraic or transcendental equations for the undetermined coefficients with multiple roots, which is required to complete calculation of the solution by several earlier modified recursion schemes using the ADM. The approximate solution is computed in the form of series with easily calculable components. The effectiveness of the proposed approach is tested by considering four examples and results are compared with previous known results.
Randhir Singh, Jitendra Kumar, and Gnaneshwar Nelakanti
Copyright © 2012 Randhir Singh et al. All rights reserved.

Solution of Nonlinear VolterraFredholm Integrodifferential Equations via Hybrid of BlockPulse Functions and Lagrange Interpolating Polynomials
Mon, 10 Dec 2012 12:42:49 +0000
http://www.hindawi.com/journals/ana/2012/868279/
An efficient hybrid method is developed to approximate the solution of the highorder nonlinear VolterraFredholm integrodifferential equations. The properties of hybrid functions consisting of blockpulse functions and Lagrange interpolating polynomials are first presented. These properties are then used to reduce the solution of the nonlinear VolterraFredholm integrodifferential equations to the solution of algebraic equations whose solution is much more easier than the original one. The validity and applicability of the proposed method are demonstrated through illustrative examples. The method is simple, easy to implement and yields very accurate results.
Hamid Reza Marzban and Sayyed Mohammad Hoseini
Copyright © 2012 Hamid Reza Marzban and Sayyed Mohammad Hoseini. All rights reserved.

A Note on Fourth Order Method for Doubly Singular Boundary Value Problems
Wed, 05 Dec 2012 17:29:24 +0000
http://www.hindawi.com/journals/ana/2012/349618/
We present a fourth order finite difference method for doubly singular boundary value problem with boundary conditions and , where , , and are finite constants. Here and is allowed to be discontinuous at the singular point . The method is based on uniform mesh. The accuracy of the method is established under quite general conditions and also corroborated through one numerical example.
R. K. Pandey and G. K. Gupta
Copyright © 2012 R. K. Pandey and G. K. Gupta. All rights reserved.

Discrete Gamma (Factorial) Function and Its Series in Terms of a Generalized Difference Operator
Tue, 13 Nov 2012 15:01:55 +0000
http://www.hindawi.com/journals/ana/2012/780646/
The recent theory and applications of difference operator introduced in (M. Maria Susai Manuel et al., 2012) are enriched and extended with a useful tool for finding the values of various series of discrete gamma functions in number theory. Illustrative examples show the effectiveness of the obtained results in finding the values of various gamma series.
G. Britto Antony Xavier, V. Chandrasekar, S. U. Vasanthakumar, and B. Govindan
Copyright © 2012 G. Britto Antony Xavier et al. All rights reserved.

The Optimal Error Estimate of Stabilized Finite Volume Method for the Stationary NavierStokes Problem
Sun, 11 Nov 2012 07:27:54 +0000
http://www.hindawi.com/journals/ana/2012/251908/
A finite volume method based on stabilized finite element for the twodimensional
stationary NavierStokes equations is analyzed. For the
element, we obtain the optimal error estimates of the finite volume solution and . We also provide some numerical examples
to confirm the efficiency of the FVM. Furthermore, the effect of initial value for iterative method
is analyzed carefully.
Guoliang He, Jian Su, and Wenqiang Dai
Copyright © 2012 Guoliang He et al. All rights reserved.