Error Estimation for Boundary Element Analysis

Rencis, Joseph J.; Jong, K.-Y.

doi:10.1061/(asce)0733-9399(1989)115:9(1993)

Cited by 22 publications

(7 citation statements)

References 19 publications

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“…In the context of the boundary element analysis, the boundary L 2 norm is usually preferred, as it can be easily evaluated from the boundary solution alone in contrast to the energy norm which requires solutions to be known at internal points as well (Rencis and Jong, 1989). The absolute error in the approximate solution of function v is defined as…”

Section: Error Indicatorsmentioning

confidence: 99%

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Dual reciprocity boundary element analysis of transient advection‐diffusion

Singh

Tanaka²

2003

Int Jnl of Num Meth for HFF

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This paper presents an application of the dual reciprocity boundary element method ( DRBEM) to transient advection-diffusion problems. Radial basis functions and augmented thin plate splines (TPS) have been used as coordinate functions in DRBEM approximation in addition to the ones previously used in the literature. Linear multistep methods have been used for time integration of differential algebraic boundary element system. Numerical results are presented for the standard test problem of advection-diffusion of a sharp front. Use of TPS yields the most accurate results. Further, considerable damping is seen in the results with one step backward difference method, whereas higher order methods produce perceptible numerical dispersion for advection-dominated problems.

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Section: Error Indicatorsmentioning

confidence: 99%

“…To obtain a more transparent measure of solution error, exact relative L 2 error (in per cent) can be defined as (Rencis and Jong, 1989) h…”

Section: Error Indicatorsmentioning

confidence: 99%

Dual reciprocity boundary element analysis of transient advection‐diffusion

Singh

Tanaka²

2003

Int Jnl of Num Meth for HFF

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“…Interval boundary element method (IBEM) [20] has been developed to account for the uncertainty in boundary conditions, integration error, and truncation error. Global discretization error in the integral equations for solutions to harmonic and bi-harmonic problems [21] and for BEM [22,23] was shown to converge. This paper discusses the interval treatment of local discretization error in IBEM illustrated on a torsion problem.…”

Section: Introductionmentioning

confidence: 95%

Local discretization error bounds using interval boundary element method

Zalewski

Mullen

2008

Numerical Meth Engineering

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SUMMARYIn this paper, a method to account for the point-wise discretization error in the solution for boundary element method is developed. Interval methods are used to enclose the boundary integral equation and a sharp parametric solver for the interval linear system of equations is presented. The developed method does not assume any special properties besides the Laplace equation being a linear elliptic partial differential equation whose Green's function for an isotropic media is known. Numerical results are presented showing the guarantee of the bounds on the solution as well as the convergence of the discretization error.

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“…The transformed boundary integral equations are then solved by approximating the true solution over discrete boundaries, thus introducing the discretization error. Although discretization error estimates have been made for BEM [1,2] the worst case bounds on the local discretization error have been computed only for the Laplace problem [3].…”

Section: Introductionmentioning

confidence: 99%