The similarity transform for the steady three-dimensional Navier-Stokes equations of flow between two stretchable disks gives a system of nonlinear ordinary differential equations. In this article, the variational iteration method was used for solving these equations. The results have been compared with the numerical results. This article depicts that the VIM is an efficient and powerful method for solving nonlinear differential equations. This method is applicable to strongly and weakly nonlinear problems. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010
sábado, 17 de octubre de 2009
Variational iteration method for solving three-dimensional Navier-Stokes equations of flow between two stretchable disks
The similarity transform for the steady three-dimensional Navier-Stokes equations of flow between two stretchable disks gives a system of nonlinear ordinary differential equations. In this article, the variational iteration method was used for solving these equations. The results have been compared with the numerical results. This article depicts that the VIM is an efficient and powerful method for solving nonlinear differential equations. This method is applicable to strongly and weakly nonlinear problems. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010
An improved compact finite difference scheme for solving an N-carrier system with Neumann boundary conditions
Recently, we have developed a higher-order and unconditionally stable compact finite difference scheme for solving a model of energy exchanges in an N-carrier system with Neumann boundary conditions, which extends the concept of the well-known parabolic two-step model for microheat transfer. However, the combined compact finite difference scheme for the boundary is second-order accurate. Unfortunately, our statement in (Dai and Tzou, Numer Methods Partial Differential Equation, Zhao et al., Numer Methods Partial Differential Equations 23 (2007), 949-959.), that it is a fourth-order scheme is inaccurate, because the scheme was multiplied by [Delta]x2 in the derivation. In this article, we develop a new combined compact finite difference scheme for the boundary, which is third-order accurate. Using the exact same proof for stability analysis as in (Dai and Tzou, Numer Methods Partial Differential Equations), the new scheme is unconditionally stable with respect to the initial conditions and source terms. The improved compact scheme is then tested by a numerical example. Results show that the convergence rate with respect to the spatial variable from the new scheme is higher and the solution is much more accurate, when compared with those obtained using our previous compact scheme in (Dai and Tzou, Numer Methods Partial Differential Equations). © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010
An optimization-based domain decomposition method for numerical simulation of the incompressible Navier-Stokes flows
This article is concerned about an optimization-based domain decomposition method for numerical simulation of the incompressible Navier-Stokes flows. Using the method, an classical domain decomposition problem is transformed into a constrained minimization problem for which the objective functional is chosen to measure the jump in the dependent variables across the common interfaces between subdomains. The Lagrange multiplier rule is used to transform the constrained optimization problem into an unconstrained one and that rule is applied to derive an optimality system from which optimal solutions may be obtained. The optimality system is also derived using "sensitivity" derivatives instead of the Lagrange multiplier rule. We consider a gradient-type approach to the solution of domain decomposition problem. The results of some numerical experiments are presented to demonstrate the feasibility and applicability of the algorithm developed in this article. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010
Residual-based a posteriori error estimator for the mixed finite element approximation of the biharmonic equation
A reliable and efficient residual-based a posteriori error estimator is derived for the Ciarlet-Raviart mixed finite element method for the biharmonic equation on polygonal domains. The performance of the estimator is illustrated by numerical experiments. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010
Convergence of the interpolated coefficient finite element method for the two-dimensional elliptic sine-Gordon equations
An interpolated coefficient finite element method is presented and analyzed for the two-dimensional elliptic sine-Gordon equations with Dirichlet boundary conditions. It is proved that the discretization scheme admits at least one solution, and that a subsequence of the approximation solutions converges to an exact solution in L2-norm as the mesh size tends to zero. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010
Finite element approximation of coupled seismic and electromagnetic waves in fluid-saturated poroviscoelastic media
This work presents a collection of global and iterative finite element procedures for the numerical approximation of coupled seismic and electromagnetic waves in 2D bounded fluid-saturated porous media, with absorbing boundary conditions at the artificial boundaries. The equations being analyzed are the coupled Biot's equations of motion and Maxwell equations in the diffusive range. Both seismoelectric and electroseismic coupling are simultaneously included and analyzed in the model. The case of compressional and vertically polarized shear waves coupled with the transverse magnetic polarization (PSVTM-mode) is analyzed in detail, including the derivation of a priori error estimates on the global finite element procedure and results on the convergence of a domain decomposition iterative algorithm. Later, the corresponding results for the case of horizontally polarized shear waves coupled with the transverse electric polarization (SHTE-mode) are stated. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010
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