摘要:

AbstractIn this paper we consider a class of inverse problems in which an unknown function,c(.), is to be determined from a parabolic initial‐value problem, with overposed Dirichlet data along a portion of the boundary. A mapping between the overposed data and the unknown coefficient is obtained in the form of a singular integral equation. This is solved by iteration, and the resulting fixed point is shown to be the solution of the inverse problem. Sufficient conditions for convergence of this method, as well as an extension to the case of an unknown thermal conductivity, are give

ISSN:0749-159X    

DOI:10.1002/num.1690060102

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY

摘要:

AbstractA finite element method is used for the computation of entropy solutions to the transonic full potential equation. Physically correct solutions with sharp and correctly placed shocks were obtained. (AMS (MOS) 1980 Mathematics subject classifications: 65N30, 76N15, 35M05, 76H05, 49D10, 35A40, 35L67.)

ISSN:0749-159X    

DOI:10.1002/num.1690060103

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY

摘要:

AbstractMoving fronts and pulses appear in many engineering applications like flame propagation and a falling liquid film. Standard computation methods are inappropriate since the problem is defined over an infinite domain and a steady‐state solution exists only for a certain front velocity. This work presents a transformation that converts the original problem into a boundary‐value problem within a finite domain, in a way that preserves the behavior at the boundaries. Good low‐order approximations can be obtained as demonstrated by two examples. In another approach, a central element of adjustable length is incorporated into a three‐element structure where the edge‐elements obey known asymptotic solutions. That yields multiplicity of travelling fronts in an infinite domain but it successfully approximates standing wave solutions in a finite domain. The approximate solutions are shown to obey the qualitative features known for the exact solutions, like asymptotic solutions or the bifurcation set–the boundary where a new solution emerges or

ISSN:0749-159X    

DOI:10.1002/num.1690060104

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY

摘要:

AbstractIn this paper we consider piecewise linear finite element approximations to the problem of planar linear elasticity, and present some new estimates for the pointwise (L∞) superconvergence of a recovered gradient function to the gradient of the true solution. This extends to linear elasticity the previous work of the present and other authors onL∞results for Poisson problems, and at the same time, to theL∞norm the previousL2results of the authors for linear elast

ISSN:0749-159X    

DOI:10.1002/num.1690060105

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY

摘要:

AbstractWe consider a boundary element (BE) Algorithm for solving linear diffusion desorption problems with localized nonlinear reactions. The proposed BE algorithm provides an elegant representation of the effect of localized nonlinear reactions, which enables the effects of arbitrarily oriented defect structures to be incorporated into BE models without having to perform severe mesh deformations.We propose a one‐step recursion procedure to advance the BE solution of linear diffusion localized nonlinear reaction problems and investigate its convergence properties. The separation of the linear and nonlinear effects by the boundary integral formulation enables us to consider the convergence properties of approximations to the linear terms and nonlinear terms of the boundary integral equation separately.For the linear terms we investigate how the degree of piecewise polynomial collocation in space and the size of the spatial mesh relative to the time step affects the accumulation of errors in the one‐step recursion scheme. We develop a novel convergence analysis that combines asymptotic methods with Lax's Equivalence Theorem. We identify a dimensionless meshing parameter θ whose magnitudé governs the performance of the one‐step BE schemes. In particular, we show that piecewise constant (PWC) and piecewise linear (PWL) BE schemes are conditionally convergent, have lower asymptotic bounds placed on the size of time steps, and which display excess numerical diffusion when small time steps are used. There is no asymptotic bound on how large the tie steps can be–this allows the solution to be advanced in fewer, larger time steps. The piecewise quadratic (PWQ) BE scheme is shown to be unconditionally convergent; there is no asymptotic restriction on the relative sizes of the time and spatial meshing and no numerical diffusion. We verify the theoretical convergence properties in numerical examples. This analysis provides useful information about the appropriate degree of spatial piecewise polynomial and the meshing strategy for a given problem.For the nonlinear terms we investigate the convergence of an explicit algorithm to advance the solution at an active site forward in time by means of Caratheodory iteration combined with piecewise linear interpolation. We consider a model problem comprising a singular nonlinear Volterra equation that represents the effect of the term in the BE formulation that is due to a single defect. We prove the convergence of the piecewise linear Caratheodory iteration algorithm to a solution of the model problem for as long as such a solution can be shown to exist. This analysis provides a theoretical justification for the use of piecewise linear Caratheodory iterates for advancing the effects of localized

ISSN:0749-159X    

DOI:10.1002/num.1690060106

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY

ISSN:0749-159X    

DOI:10.1002/num.1690060101

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY