Adaptive r and h — r algorithms for boundary elements

Zamani, Nader G.; Sun, Weiwei

doi:10.1016/0965-9978(92)90106-p

Cited by 12 publications

(2 citation statements)

References 14 publications

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“…This approach was highly dependent on the weakness of the singularities involved in the Laplacian operator and on the existence of a grading function. Zamani and Sun [30] discussed also the implementation of r and h − r reÿnement-redistribution techniques. In Kita et al [31] a relationship between error and element size is established, and the goal is to redistribute the error on the elements.…”

Section: Introductionmentioning

confidence: 98%

New approaches for error estimation and adaptivity for 2D potential boundary element methods

Jorge

Ribeiro

Fisher

2002

Numerical Meth Engineering

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SUMMARYThis work presents two new error estimation approaches for the BEM applied to 2D potential problems. The ÿrst approach involves a local error estimator based on a gradient recovery procedure in which the error function is generated from di erences between smoothed and non-smoothed rates of change of boundary variables in the local tangential direction. The second approach involves the external problem formulation and gives both local and global measures of error, depending on a choice of the external evaluation point. These approaches are post-processing procedures. Both estimators show consistency with mesh reÿnement and give similar qualitative results. The error estimator using the gradient recovery approach is more general, as this formulation does not rely on an 'optimal' choice of an external parameter. This work presents also the use of a local error estimator in an adaptive mesh reÿnement procedure. This r-reÿnement approach is based on the minimization of the standard deviation of the local error estimate. A non-linear programming procedure using a feasible-point method is employed using Lagrange multipliers and a set of active constraints. The optimization procedure produces ÿner meshes close to a singularity and results that are consistent with the problem physics.

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Section: Introductionmentioning

confidence: 98%

New approaches for error estimation and adaptivity for 2D potential boundary element methods

Jorge

Ribeiro

Fisher

2002

Numerical Meth Engineering

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“…The equidistribution mesh method was ®rst studied by Carey and Kennon 9 for the twodimensional boundary element solution to Laplace's equation, and later it was applied to many physical and engineering problems by many authors, such as in fracture mechanics 8,10 and in free-surface¯ow. 11 In all those approaches, the mesh is generated with a large concentration about the area of large solution variation, and an associated error function de®ned on the boundary is equally distributed on each boundary element.…”

Section: Introductionmentioning

confidence: 99%