摘要:

AbstractWe presenta priorianda posterioriestimates for the error between the Galerkin and a discretized Galerkin method for the boundary integral equation for the single layer potential on the square plate. Using piecewise constant finite elements on a rectangular mesh we study the error coming from numerical integration. The crucial point of our analysis is the estimation of some error constants, and we demonstrate that this is necessary if our methods are to be used. After the determination of these constants we are in the position to prove invertibility and quasioptimal convergence results for our numerical scheme, if the chosen numerical integration formulas are sufficiently precise. © 1992 John Wiley&Sons, Inc

ISSN:0749-159X    

DOI:10.1002/num.1690080502

出版商:John Wiley&Sons, Inc.    

年代:1992

数据来源: WILEY

摘要:

AbstractSome approximate methods for solving linear hyperbolic systems are presented and analyzed. The methods consist of discretizing with respect to time and solving the resulting hyperbolic system for fixed time by least squares finite element methods. An analysis of least squares approximations is given, including optimal order estimates for piecewise polynomial approximation spaces. Numerical results for the inviscid Burgers' equation are also presented. © 1992 John Wiley&Sons, Inc

ISSN:0749-159X    

DOI:10.1002/num.1690080503

出版商:John Wiley&Sons, Inc.    

年代:1992

数据来源: WILEY

摘要:

AbstractWe discuss multigrid methods and multilevel preconditioners for first kind boundary integral equations with weakly and hypersingular kernels. We find that the number of iterations needed is bounded or grows no worse than logarithmically in the numbers of unknowns. We also discuss the complexity for parallel implementations.

ISSN:0749-159X    

DOI:10.1002/num.1690080504

出版商:John Wiley&Sons, Inc.    

年代:1992

数据来源: WILEY

摘要:

AbstractThis article concerns the development of energy‐based variational formulations and their corresponding finite element–boundary element Rayleigh–Ritz approximations for solving the time‐harmonic vibration and scattering problem of an inhomogeneous penetrable fluid or solid object immersed in a compressible, inviscid, homogeneous fluid. The resulting coupled finite element and boundary integral methods (FEM‐BEM) have the following attractive features: (1) Separate direct and complementary variational principles lead naturally to several alternative structure variable and fluid variable methodologies. (2) The solution in the exterior region is represented by a combined single‐ and double‐layer potential which ensures the validity of the methods for all wave numbers; even though this representation introduces hypersingular integrals, for actual computations the hypersingular operator may be rewritten in terms of single‐layer potentials, which can be integrated by standard techniques. (3) Since the discretized equations for the interior region and for the boundary are derived from the first variation of bilinear functionals the resulting algebraic systems of equations are always symmetric. In addition, the transition conditions across the interface are natural. This allows one to approximate the solutions within the interior and exterior regions independently, without imposing any bound

ISSN:0749-159X    

DOI:10.1002/num.1690080505

出版商:John Wiley&Sons, Inc.    

年代:1992

数据来源: WILEY

摘要:

AbstractThe defect correction technique, based on the Galerkin finite element method, is analyzed as a procedure to obtain highly accurate numerical solutions to second‐order elliptic boundary value problems. The basic solutions, defined over a rectangular region Ω, are computed using continuous piecewise bilinear polynomials on rectangles. These solutions areO(h2) accurate globally in the second‐order discrete Sobolev norm. Corrections to these basic solutions are obtained using higher‐order piecewise polynomials (Lagrange polynomials or splines) to form defects. AnO(h2) improvement is gained on the first correction. The lack of regularity of the discrete problems (beyond the second‐order Sobolev norm) makes it impossible to retain this order of improvement, but for problems satisfying certain periodicity conditions, straightforward arbitrary accuracy is obtained, since these problems possess high‐order regularity. © 1992 John Wile

ISSN:0749-159X    

DOI:10.1002/num.1690080506

出版商:John Wiley&Sons, Inc.    

年代:1992

数据来源: WILEY

摘要:

AbstractThis work develops a procedure for representing multimaterial interfaces in finite difference models. The boundary separating the two materials can be on or between a row of nodes. The development is validated by embedding the boundary between two regions in a single, larger region and comparing the results. The development is facilitated by the use of a physically based notation that represents the displacement approximations in terms of rigid‐body rotations and strain gradient quantities that produce the displacements. Four example problems are presente

ISSN:0749-159X    

DOI:10.1002/num.1690080507

出版商:John Wiley&Sons, Inc.    

年代:1992

数据来源: WILEY

ISSN:0749-159X    

DOI:10.1002/num.1690080501

出版商:John Wiley&Sons, Inc.    

年代:1992

数据来源: WILEY