摘要:

AbstractCoupling techniques are essential to combining different numerical methods together for the purpose of solving an elliptic boundary value problem. By means of nonconforming constraints, the combinations of various Lagrange finite element methods often cause reduced rates of convergence. In this article, we present a method using penalty plus hybrid technique to match different finite element methods such that the optimal convergence rates in the ‖ · ‖hand zero norms of errors of the solution can always be achieved. Also, such a coupling technique will lead to an optimal asymptotic condition number for the associated coefficient matrix. Moreover, this study can easily be extended for combining the finite difference method with the finite element method to also yield the optimal rate of converg

ISSN:0749-159X    

DOI:10.1002/num.1690080301

出版商:John Wiley&Sons, Inc.    

年代:1992

数据来源: WILEY

摘要:

AbstractAn important class of problems in mathematical physics involves equations of the form −∇ · (A∇ϕ) =f. In a variety of problems it is desirable to obtain an accurate approximation of the flow quantityu= −A∇ϕ. Such an accurate approximation can be determined by the mixed finite element method. In this article the lowest‐order mixed method is discussed in detail. The mixed finite element method results in a large system of linear equations with an indefinite coefficient matrix. This drawback can be circumvented by the hybridization technique, which leads to a symmetric positive‐definite system. This system can be solved efficiently by the preconditioned conjugate gradient method. After approximating u by the lowest‐order mixed finite element method, streamlines and residence times can be determined easily and accurately by computations at

ISSN:0749-159X    

DOI:10.1002/num.1690080302

出版商:John Wiley&Sons, Inc.    

年代:1992

数据来源: WILEY

摘要:

AbstractThe combined approach of linearization and splitting up is used for devising new algorithms to solve a one‐dimensional Burgers' equation. Two schemes are discussed and the computed solutions are compared with the exact solution. For this problem it is found that the schemes proposed yield excellent numerical results for Reynolds number R ranges from 50 up to 1500. The schemes were also tested for another problem whose R = 10000. In this case a filtering technique is used to overcome the nonlinear instabilit

ISSN:0749-159X    

DOI:10.1002/num.1690080303

出版商:John Wiley&Sons, Inc.    

年代:1992

数据来源: WILEY

摘要:

AbstractWe derive an algorithm for solving the initial value problem forut= ½σ2uxx+f(u)ux. The approach is based on the representation of the solution to the above equation in the form of the functional of Brownian motion. For small σ we get the approximation forut=f(u)ux. A comparison with the random choice method is illustrated by the numerical examp

ISSN:0749-159X    

DOI:10.1002/num.1690080304

出版商:John Wiley&Sons, Inc.    

年代:1992

数据来源: WILEY

摘要:

AbstractA multivariate box spline framework for the formulation of numerical methods for partial differential equations has been constructed. In particular, a fourth‐order Galerkin method and a second‐order collocation method were derived and applied to a test problem (classical Poisson equation on a square). The examples indicate that accuracy compares favorably with standard methods and the success of iterative schemes suggests an underlying stabilizing eff

ISSN:0749-159X    

DOI:10.1002/num.1690080305

出版商:John Wiley&Sons, Inc.    

年代:1992

数据来源: WILEY