摘要:

AbstractSuperconvergent error estimates inl2(H1) andl∞(H1) norms are derived for recovered gradients of finite difference in time/piecewise linear Galerkin approximations in space for linear and quasinonlinear parabolic problems in two space dimensions. The analysis extends previous results for elliptic problems to the parabolic context, and covers problems in regions with nonsmooth boundaries under certain assumptions on the regularity of the solutions. © 1994 John Wiley&Sons, I

ISSN:0749-159X    

DOI:10.1002/num.1690100303

出版商:John Wiley&Sons, Inc.    

年代:1994

数据来源: WILEY

摘要:

AbstractSteady incompressible flow around objects in general coordinates is investigated. First, an overview of the popular approaches to discretize incompressible flow problems in general coordinates is given. It has been chosen to solve the equations on a staggered grid with contravariant flux unknowns and pressure as primitive variables. A solution method multigrid is used, with a line smoother able to deal with stretched cells. For flow problems around objects solved with a single block discretization periodic boundary, conditions are prescribed and adaptations for the discretization and the multigrid method are given. Steady flow around a circular cylinder and around an ellipse are presented. © 1994 John Wiley&Sons, Inc

ISSN:0749-159X    

DOI:10.1002/num.1690100304

出版商:John Wiley&Sons, Inc.    

年代:1994

数据来源: WILEY

摘要:

AbstractWe study the Stokes problem by using a mixed finite element method introduced by Stenberg [Numer. Math.56, 827 (1990)] and adapt it to the splitting introduced by Canuto and Sacchi Landriani [Numer. Math.50, 217 (1986)] and Chinosi and Comodi [Numer. Methods Partial Different. Equations7, 363 (1991)], by using the incompressibility condition to implicitly define a boundary condition for the pressure. © 1994 John Wiley&Sons, Inc

ISSN:0749-159X    

DOI:10.1002/num.1690100305

出版商:John Wiley&Sons, Inc.    

年代:1994

数据来源: WILEY

摘要:

AbstractWe analyze a Crank‐Nicolson scheme for a family of nonlinear parabolic partial differential equations. These equations cover a wide class of models of excitability, in particular the Hodgkin Huxley equations. To do the analysis, we have in mind the general discretization framework introduced by López‐Marcos and Sanz‐Serna [inNumerical Treatment of Differential Equations, K. Strehemel, Ed., Teubner‐Texte zur Mathematik, Leipzig, 1988, p. 216]. We study consistency, stability and convergence properties of the scheme. We use a technique of modified functions, introduced by Strang [Numer. Math.6, 37 (1964)], in the study of consistency. Stability is derived by means of the energy method. Finally we obtain existence and convergence of numerical approximations by means of a result due to Stetter (Analysis of Discretization Methods for Ordinary Differential Equations. Springer‐Verlag, Berlin, 1973). We show that the method has optimal order of accuracy in the discreteH1norm. © 1994 John Wile

ISSN:0749-159X    

DOI:10.1002/num.1690100306

出版商:John Wiley&Sons, Inc.    

年代:1994

数据来源: WILEY

摘要:

AbstractThe Jacobi polynomial collocation method is extended to two and three dimensions by superimposing the individual one‐dimensional expansions. Two innovative ideas are introduced in this article. The first is the cornerless/edgeless computational grid, and the second is the modified compressibility method, which is an iterative pressure solver. To evaluate the new method's applicability in solving the Navier‐Stokes equation, the lid‐driven cavity flow problem was solved. Two configurations were considered, the square cavity and the rectangular cavity with an aspect ratio of 2. A comparison of the center‐line velocity profiles from two‐ and three‐dimensional simulations at a Reynolds number of 1000 is provided for each of the configurations. The center‐line velocity comparisons showed good quantitative agreement with previous studies. © 1994 John W

ISSN:0749-159X    

DOI:10.1002/num.1690100307

出版商:John Wiley&Sons, Inc.    

年代:1994

数据来源: WILEY

摘要:

AbstractUnder mild conditions a certain subspaceM, consisting of functions which are analytic in a simply connected domain Ω and continuous on the boundary Gamma;, is shown to have real parts which are dense, in the sup norm, in the set of all solutions to the Dirichlet problem for continuous boundary data. Similar results hold forLpboundary data. Numerical solutions of sample Dirichlet problems are computed. © 1994 John Wiley&Sons, In

ISSN:0749-159X    

DOI:10.1002/num.1690100308

出版商:John Wiley&Sons, Inc.    

年代:1994

数据来源: WILEY

摘要:

AbstractThe anomalous infinite propagation speeds in the classical parabolic flow equations are removed by the inclusion of a small amount of fluid elasticity or viscous stress relaxation. The inclusion of such effects results in a hyperbolic system of equations with a complete set of characteristic equations. The directional characteristic equations are used to give insights into the appropriate boundary molecules to be used in finite difference numerical schemes. © 1994 John Wiley&Sons, Inc

ISSN:0749-159X    

DOI:10.1002/num.1690100309

出版商:John Wiley&Sons, Inc.    

年代:1994

数据来源: WILEY

摘要:

AbstractInitial‐boundary value problems for nonlinear differential‐functional equations are considered. A general class of lines method is investigated. The Perron‐type estimation for the right‐hand side of the equation with respect to the functional argument is assumed. The proof of the convergence is based on a comparison theorem for differential‐difference inequalities. A numerical example is given. © 1994 John Wiley

ISSN:0749-159X    

DOI:10.1002/num.1690100310

出版商:John Wiley&Sons, Inc.    

年代:1994

数据来源: WILEY

ISSN:0749-159X    

DOI:10.1002/num.1690100302

出版商:John Wiley&Sons, Inc.    

年代:1994

数据来源: WILEY